₦airaland Forum

https://www.youtube.com/watch?v=RtVuLThyGzI
Non exact differential equations can be solved by introducing a function into the equation that will make it exact, then the Differential Equation can be solved using the exact method, as a matter of fact for every differential equation M(x,y)dx+N(x,y)Dy=0 there exist F(x), F(y) and F(x,y) that can serve as the integrating factor for the differential equation

https://www.youtube.com/watch?v=RtVuLThyGzI

https://www.youtube.com/watch?v=NOdkLzkA_TM An homogeneous differential equation has no composite function like yy' or siny or √y in it, they are reducible into separable differential equation by setting y=vx, then the separable differential equation is solved to obtain its general solution.
2xyy'=(y^2)-(x^2) is an example of such as we can clean it up to get y' by itself, you also notice that all functions involved are expressed to the same power.

https://www.youtube.com/watch?v=NOdkLzkA_TM

https://www.youtube.com/watch?v=1gxPc-PxBEE The first type of differential equation that will be introduced is probably going to be a separable Ordinary Differential Equation, the variables in this type of differential equation is required to be separated so that the integral of both side can evaluated to obtain the general solution of the differential equation. In case an initial value is given, then the constant can be obtained to write the specific solution of the DE

https://www.youtube.com/watch?v=1gxPc-PxBEE

https://www.youtube.com/watch?v=mxdIf3IXmfs Exact differential equations may not be linear or homogenous such that you cannot simply separate the variables, after rewriting the differential equation in the form Mdx+Ndy=0, you will go on and test for exactness, if the test for exactness does not fail, set a function U(x,y)=integral(Mdx)+k(y), note that k is not a constant of integration, the function U(x,y) is the original function that yield the differential equation. Understanding total differential is the key to understanding exact differential equation.

https://www.youtube.com/watch?v=mxdIf3IXmfs