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Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 9:07am On Aug 05, 2015

Karmanaut:
My oga, I hail.

hmmm c boss dey call boy. oga, bros, no washing pls....
respects man.

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 9:06am On Aug 05, 2015

Laplacian:
i feel ur efforts bro, kudos!!...enjoy urself!!!

yea man, naGodwin...... nice works sir.

Education › Re: Nine Surprising Facts About Breasts You Probably Didn’t Know by agentofchange1(m): 8:49am On Aug 05, 2015

more

# Guys experience pen^s er*ction(a.k.a) buran tashi ) quicker when staring at breast than any other part of a Lady's body

#some men this days sucks the breast more than infants

which is why some ladies this days make sure they expose 20% or 45% some 75% or even 95% (bt y not 100%) of their boobs to the masses 2 behold (hmm)

girls y na y? , y r u killing us?

#safe. the. boy. child.... reserve ur boobs 4ur husband /infant'

#shalom

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Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:55pm On Aug 04, 2015

#just. drinking. Garri and observing

happy solving guys...

@ Laplacian ( m ), Karmanaut greetings in CAPITAL letters

Education › Re: Scientists Will Soon Be Able To Raise The Dead by agentofchange1(m): 3:03pm On Aug 03, 2015

Fringe !!

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 12:16pm On Aug 03, 2015*

jackpot:
Find the inverse laplace transform of 1/(s^5+a^5)

tags: Laplacian, agentofchange1, doubleDx, dejt4u, Alphamaximus, jaryeh

considering the denominator

s^5 +a^5

in general

xⁿ + yⁿ

=(x+y) £ y^k* x^(n-1-k) for k=0,1 2, . . . ,(n-1)

where £ = sigma (summation)

does that ring a bell?. I know say you na Prof.

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 9:21am On Aug 03, 2015

Antoinne:
There seems to be a mistake in the first two lines in the first picture with y². Would affect the final answer significantly.

oh yeah, my bad , just noticed that now ...will upload corrected solutions sir

thanks once again.

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:34am On Aug 03, 2015*

m kinda busy now, remaining solutions might come later ,
av solved them already , just 2uplaod ...

or my bosses in d hus can do that ,

#Slalom.

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:24am On Aug 03, 2015*

possibilita:
thank u very much bros

UWC man

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Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:09am On Aug 03, 2015*

possibilita:
yes that's hw 1c is written

ok here

Q1c
y' = (3y² +2xy)/(2xy+x² ).. ......(B)

Set y=vx. V= y/x

=> y'=xv' +v ...(E)

Equate with (B) above
We have

Xv'+v= [3(vx)^2 +2x(vx)]/[2x(vx) +x^2]

=( 3x^2 v^2 +2x^2 v )/(2x^2 v +x^2)

Pull out ' x^2 '

=> xv' =(3v^2 +2v) /(2v+1). - v

= xv '= (3v^2 +2v -2v^2 -v)/(2v+1)

Xdv/dx = (v^2 +v) /(2v +1)

=>( 2v+1)dv/(v^2 +v) = dx/x

Taking integral on both sides yields

In(v^2 +v)=lnx + lnC

Or v^2 +v = CX

Since y/x = v

hence we have

=(y/x)^2 + (y/x) = CX

ii)

y' = y/x + xsin(y/x)

Let vx=y , v= y/x

Xv'+ V = y'

We get

xv' +v = v + xsinv .

Or v'= sinv

By separating variables

=> (1/sinv)dv = dx

On integrating both sides

=> In[tan(v/2)] = x+c

Or tan(v/2)= exp(x+c)

Or v/2 =arctan[exp(c+x)]

Or v= 2arctan[ e^c *e^x]

Since v=y/x

=>y/x = 2arctan(Ke^x)

(Where k= e^c)

Hence

Ans:y=2xarctan(Ke^x)

That's it man.

3 Likes 1 Share

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:10pm On Aug 02, 2015*

Q2 a i

****Solution****
First standardise by dividing through by '(x+1)' to be of
the form
Y' +py=q ..(where p & q are functions of x)
=> y' -y/(x+1) = e^x/(x+1) ......(*)
Integrating factor IF
= e^($pdx)
Evaluating $pdx
=> $-dx /(x+1) =-ln(x+1) =ln[1/(x+1)]
Thus IF= e^ln[1/(x+1)]
By definition, e^lna =a
Thus, IF=1/(x+1)
Now on multiplying IF by (*) , we get
D(y/(x+1)= e^x
Integrating both sides yields
Y/(x+1)= e^x+ C
Hence. Y=(x+1)(e^x + C)

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 4:58pm On Aug 02, 2015*

possibilita:
Pls help me on these

Q 1a

(i) given y^2 =Ax^2 + Bx +c

We need three derivatives (since, we Gat 3unknowns)

=>2yy'=2Ax+B

Again

=>2(y')^2 +2yy" = 2A

Or (y') ^2 +yy"=A

Again,

=>2y"*y' +y"*y' +y*y"'

Or 3y' y"+yy"'=0

ii) y=Ax+A^2..... (*)

y'=A

Thus we have

Y= xy'+(y') ^2

Or y=xdy/dx +(dy /dx)^2

b (i)

pix below

1c) m I don't think its a DR except it's written like this

(2xy + x^2 )y' = 3y^2 + 2xy is that ?

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Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 3:18pm On Aug 02, 2015

My eyes are seeing things, Good job guys....

Happy sunday

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 12:25pm On Aug 02, 2015

possibilita:
I jst wish thid calculus is optional,God this course is a world of his own,I have bEen try to solve evrytin on that paper over 2weeks now but can't while my lecturer is hoping we solve them all and submit tomoro and also use them to prepare for both test and Exam I jst feel all the time spent on this maths are wasted,afterall I have no root in calculus and now advance calculus is chipping my ass off God pls help me oh

Is OK bro post your question here

www.nairaland.com/1147658/nairaland-mathematics-clinic/184#36508620

M not always online.

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 6:35pm On Aug 01, 2015

check that #2 a (ii)
@ d R HS wrinten x^5 -2x^3. ...
cant c it clearly type out .
asap.

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 6:29pm On Aug 01, 2015

possibilita:
1.Solve d following by method of seperating. Variables

dy/dx= x(2logx+1)/(siny +ycosy)

=> (siny+ycosy) dy =(2xlnx+x) dx

take integral

=> ysiny=1/2 x^2lnx^2 + K

hrnce y= cscx (x^2lnx) + k

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 3:46pm On Aug 01, 2015

possibilita:
that's hw we saw it,d questions are in the pic below

oh, ok. u didn't type the question well.

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 1:27pm On Aug 01, 2015*

possibilita:
1.Solve d following by method of seperating. Variables

dy/dx= x(2logx+1)/siny + ycosy

X^4 dy/dx + x^3 y =-sec(xy)

recheck these questions , m not sure of it validity, as to whether the variables could be separated except other methods. (,eps. d second 1)

Asap.

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 1:21pm On Aug 01, 2015

possibilita:
2.Solve the linear differential Equation

(X^3 - x)dy/dx - (3x^2 - 1)y=x^5 - 2x

Dividing through by '(x^3 -x)'

=>y' -[(3x^2 -1)/(x^3-x)] y = (x^5 -2x)/(x^3 -x) ....(*)

Obtaining IF,

=>$pdx= $(3x^2 -1)dx /(x^3 -x)
Which takes the form $f '(x)dx /f(x) = In(f(x))

Thus we have -ln(x^3 -x)

So that IF= 1/(x^3 -x)

Taking product of IF with (*)

=>. D [ y/(x^3 -x)] = (x^5 -2x)/(x^3 -x)^2

Taking integral on sides we get

Y/(x^3 -2x)= 1/2[ 1/(x^2 -1) +3ln(1-x^2) -4lnx] +C

Or further transpose Y.

guess that's it.

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 1:01pm On Aug 01, 2015

possibilita:
2.Solve the linear differential Equation

(X+1)dy/dx - y=e^x(x+1)^2

****Solution****

First standardise by dividing through by '(x+1)' to be of the form

Y' +py=q ..(where p & q are functions of x)

=> y' -y/(x+1) = e^x/(x+1) ......(*)

Integrating factor IF
= e^($pdx)
Evaluating $pdx

=> $-dx /(x+1) =-ln(x+1) =ln[1/(x+1)]

Thus IF= e^ln[1/(x+1)]

By definition, e^lna =a
Thus, IF=1/(x+1)

Now on multiplying IF by (*) , we get

D(y/(x+1)= e^x

Integrating both sides yields

Y/(x+1)= e^x+ C

Hence. Y=(x+1)(e^x + C)

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 12:19pm On Aug 01, 2015

bestdeals0:
mah borrow u my engineering mathematics

y u dey wyn d guy na ?.

Education › Re: Are You A Graduate? Let's Know How You Made That G.P by agentofchange1(m): 11:42am On Aug 01, 2015

thatnaijabae:
that got nothing to do with studying.

its ok , I comment my reserve.

Education › Re: Are You A Graduate? Let's Know How You Made That G.P by agentofchange1(m): 11:02am On Aug 01, 2015

thatnaijabae:
I studied my books religiously and avoided boys.

hmm, I wish I cud believe this , wit d way ur pointing ur uku (@dp)

its well sha

#nagodwin

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 10:32am On Aug 01, 2015

possibilita:
help na I beg

ok , maybe later .

Education › Re: See The Cost Of Studying For 5 Years In A Nigerian University by agentofchange1(m): 9:56am On Aug 01, 2015

Ok seen.

Education › Re: Pls Help Solve The Calculus Problems by agentofchange1(m): 10:58am On Jul 30, 2015

possibilita:
2.Solve the linear differential Equation

(X+1)dy/dx - y=e^x(x+1)^2

y=(x+1)(e^x +C)

how much will you pay 4d rest...? (with full solutions)

Education › Re: Why You Must Always Have A Pen As A Student by agentofchange1(m): 7:50am On Jul 25, 2015

naijainfogalery:
This op must be a student , it doesn't happen the way you posted it here , Emeka was that guy that hardly come to class and if he manages to come, Emeka doesn't have note talkless of biro to write, of there is anyone with a less chance of making it in life its Emeka, Emeka managed to graduate from Secondary school and that was all I know about Emeka not until fast forward 2014 , I saw Emeka on TV as a special adviser to one governor in the east , as I am telling you now Emeka is so popular in that town that he has his own aides and entourage , if I choose to say his name here majority of you might have heard of him.
So my dear life doesn't work that way. There are some people that know their ways ,
Another story Victoria was an head girl back in the same school very brillant, smart, intelligent cute and very dedicated , she seems like the perfect girl with the perfect future as its just natural for things to work for her. Vic is that girl that has 10 extra biros , her notes are so neat she wouldn't even borrow you to copy, she knows the answer to almost every question . I had a crush on that babe I swear. She is too serious to even notice me. Fast forward this year, I saw Vic and I almost shed tears . victoria was doing a job that pays less than 30k a month.

So I was wondering what the hel l happened then I remembered something Emeka might not be smart but he is skilled. If u need to buy a new chinos , text book, gadget and needs a good deal call Emeka, if you need connections on anything call Emeka , he can convince a dead man to wake up, he knows every body , very friendly and got lots of skills but our Sis Vic always with book , book. Book she doesn't even give a damn about people ,

So whike in school don't work hard work smart

I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.

I have seen servants upon horses, and princes walking as servants upon the earth.

Education › Re: Nairaland Math Quiz Competition Loading...(suggestions Needed) by agentofchange1(m): 8:29pm On Jul 23, 2015

tohero:
So far, So better. However, I feel these two inputs will redefine it towards the best.

1- Organization:
--- Fixed time for posting and answering of questions.
--- measures taken for modifying answers by participants.
--- Level of Questions: In as much as I will love brain teasing mathematics questions, there is still a need to diversify them. But again, we need to take note that it is not a crime if a Statistician fails repeatedly in Computational Mathematics,its not his field. In lieu of this, I recommend Stages for the test questions. From simple Math. Questions to Brain Teasers(Reasoning). Each Stage will cross out questions from Trigonometry to Geometry, Algebra to Statistics. If need be, A tougher stage may cut across Analysis to Computational Mathematics.

In Summary, Each stage should provides a participant an average level of questions and average participation.

2--- Formatting of Questions and Answers. The issue of incorporating mathematical symbols can be alarming! Though, we can use "/=" to represent "not equal to" but can we easily find replicas for binary operations?
I once advised in the CLINIC about learning to imbibe ourself the culture of using LaTeX but no duly response, maybe the people I am talking to are already gurus using LaTeX

If Possible, Questions should be posted using LaTeX in form of Images. I hope one day Seun will endeavour to include a plugin on the site to enable us type it directly.

I hope these two points help.

For the Love of Math!

well said my guy !!

Education › Re: Nairaland Math Quiz Competition Loading...(suggestions Needed) by agentofchange1(m): 8:28pm On Jul 23, 2015

Fynestboi:
following....

my guy i greet thee
btW: is this not suppose to be on FP ?.
u guys should try do smtin.so dat more folks will be aware. ..

Education › Re: How And Why Did Newton Develop Such Complicated Mathematics? by agentofchange1(m): 6:24pm On Jul 23, 2015

@ OP GREAT PIECE
Calculus's my most romantic lover
Gat lots of applications
#team. Maths.

Education › Re: Maths Wizards Please Help On This. by agentofchange1(m): 3:56pm On Jul 22, 2015

Adrenaline123:
Thanks a lot

wc man.

Education › Re: Nairaland Mathematics Clinic by agentofchange1(m): 3:45pm On Jul 22, 2015

joywendy:
Thanks, quite an interesting read. I appreciate

Uwc dearie , Any Day.

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