I tried using the method described by the book. Setting M= y^3+2ye^x and N = (e^x+3y^2)... then taking dM/dy and dN/dx... then (dM/dy - dN/dx) / N and (dN/dx - dM/dy) / M... I don't know if my problem is that I did something wrong in the derivations but neither gives me an integration factor...
I am having issues finding the integration factor for the following two problems. I believe the second one can be solved by inspection.
1. (y^3+2ye^x)dx + (e^x+3y^2)dy = 0
2. (x-x^2-y^2)dx + (y+x^2+y^2)dy = 0
yes it is supposed to read y, y', y"... the problem is as it is written in the book... it didn't say that it was a 2nd order ODE.
Clearly the original differential eq. and it's two derivatives are linearly dependent since the determinant is zero, but I don't understand what I'm exactly supposed...
I understand that if the determinant is zero, the equations are linearly dependent, but I don't know how to go about doing the proof required to answer the problem.
I'm having a couple problems with my diff eq assignment if anyone can help me. The problem is 1. (a) show that the diff eq. for y=c1u1(x) + c2u2(x), where u1(x) and u2(x) are functions which are at least twice differentiable, may be written in determinant form as
| y u1(x) u2(x) |
| y...