Hello Guys. I study Computer Science in a private University in Nigeria and as such, I offer mathematical courses. The Lecturer in charge of the Maths method really didn't do a good job and it all looked like magic because my calculus game was weak and I barely passed it in 100 level. I was finally able to fall in love with Maths method as a result of enough preparation via Professor Leonard Calculus Videos on YouTube. I also used YouTube a lot for Numerical Analysis and Linear Algebra and they proved very useful. We just ended the semester today and I already got the courses I am to offer next semester and one among them is Elementary Differential Equation. The issue is that the channel I love on YouTube that really improved my Calculus game has a full video playlist on Ordinary Differential Equations and as a result; I want to confirm if they are both the same thing before I proceed. Mathematicians in the house; Please help. Thank you

Differential equations can be divided into Ordinary and partial Differential equations. The basic difference is
For the first one
y=F(x)
For the second one,
y=F(x,y,z,...)
Hence the ways of solving differs a bit. Yet, your basic knowledge will help you. Proceed

Ocheinstein:
Differential equations can be divided into Ordinary and partial Differential equations. The basic difference is
For the first one
y=F(x)
For the second one,
y=F(x,y,z,...)
Hence the ways of solving differs a bit. Yet, your basic knowledge will help you. Proceed

Thank you so much. I really appreciate this

ihollarmide:

Thank you so much. I really appreciate this

God bless you brother

Yes, they are the same . The ordinary differential equations I know :

1) First Order Separable Differential Equation.

This equation is of the form M(x) dx + N(y) dy = 0 where M(x) is a continuous function of x and N(y) is a continuous function of y . It is solved by separation of variables.

2) First Order Linear Differential Equation.

This equation has the standard form (dy/dx) + P(x) y = Q(x) , where P(x) and Q(x) are continous functions of x .

3) Bernoulli Equation.

This equation has the standard form (dy/dx) + P(x) y = Q(x) y^n , where n ≠ 1 & n ≠ 0 . It can be reduced to the a first order linear differential equation by an appropriate substitution. P(x) and Q(x) are continous functions of x .

4) Homogeneous Differential Equation.

This equation has the standard form M(x, y) dx + N(x, y) dy = 0 , where M(x, y) and N(x, y) are homogeneous functions of the same degree. You can solve this by using the substitution y = vx to make it separable. v is a differentiable function of x .

Martinez39:
Yes, they are the same . The ordinary differential equations I know :

Great mathematician

I love mathematics,