Integration Factors: Solving Problems

[confusedM]

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

 

[Defennder]

For the first one, try assuming in turn that the integrating factor is a function of either x or y only, then see if you can come up with it by solving a DE.

What do you mean by 2nd one being solvable by inspection?

 

[confusedM]

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 that is a function of just y or just x.

As far as the second goes, I meant that the equation needs to be modified so that the above is possible (dM/dy = dN/dx), but I can't figure out how to modify the equation around so that is possible.

The solutions are supposed to be:
1. y^3e^x+ye^(2x)=c
2. ln(x^2 + y^2) +2y - 2x = c

 

[confusedM]

never mind. I got it.