Solving Ordinary Differential Equations

1. I want to solve this ordinary diff equation:

**(1-x^2)dy/dx + 2xy = (1-x^2)^3/2 **

Here is my working:

dy/dx = (1-x^2)^3/2 - 2xy / (1-x^2)

= (1-x^2)^1/2 -2xy/(1-x^2)

It's unseparable and I can't use substitution since I can't see a (x/y), what should I do next to solve this?

**2. I also want to solve: (y-x)dy/dx + 2x + 3y = 0 **

But I get:

**dy/dx = -(2x + 3y)/(y-x)**

and I'm stuck on what to do next.

Could someone please help me? I really want to undertand how to solve these.

Thankyou for your time and help, I really do appreciate it.

Re: Solving Ordinary Differential Equations

Hello, happyfingerrs!

Divide by

Integrating factor:

. .

This one is homogeneous . . .

. .

. . which simplifies to: .

Got it?

Re: Solving Ordinary Differential Equations

Re: Solving Ordinary Differential Equations

Hello Soroban, thankyou very much for your help :) Your working was incredibly useful :)

My only remaining question is, how would you integrate v-1/v^2 + 2v + 2? Do you have to complete the square or use trig identities?

Thank you so much :)