How can I effectively solve two challenging differential equations problems?

[FaradayLaws]

Homework Statement

I have two problems from my differential equations assignment that I'm having difficulty with. I would appreciate some guidance!

Homework Equations

http://img10.imageshack.us/img10/3397/questionsk.th.jpg

The Attempt at a Solution

for no.10 I used reduction of order with the assumption that one solution is y1=e^x
I got y2=xe^x

my question is for this question do I solve the unhomogenous equation by variation of parameters to solve for the particular solution And from there use it for the General Solution ? ( yg= yh+yp.

For no.7
I multiplied by x^p y^q and found the partial derivatives My and Nx.
Inorder for it to be exact, I equated the partial derivatives and found my values for p and q. They came out to being fractions and my final solution is extremely messy with fractions. Is this is correct approach?

Thanks.

 

[HallsofIvy]

Homework Statement

I have two problems from my differential equations assignment that I'm having difficulty with. I would appreciate some guidance!

Homework Equations

http://img10.imageshack.us/img10/3397/questionsk.th.jpg

The Attempt at a Solution

for no.10 I used reduction of order with the assumption that one solution is y1=e^x
I got y2=xe^x

my question is for this question do I solve the unhomogenous equation by variation of parameters to solve for the particular solution And from there use it for the General Solution ? ( yg= yh+yp.

Yes.

for no.7
I multiplied by x^p y^q and found the partial derivatives My and Nx.
Inorder for it to be exact, I equated the partial derivatives and found my values for p and q. They came out to being fractions and my final solution is extremely messy with fractions. Is this is correct approach?

Did you get 3q= 2(p+1) and 20(q-1)= 12(p+ 3)? That's what I got. Yes, those give "messy" fractions.

Thanks.[/QUOTE]