# Thread: Find particular solution by substitution

1. ## Find particular solution by substitution

1.By substitution y = vx , show that x(x+y)dy/dx = x^2 + y^2 is y + x ln ((x-y)^2 /x) = 0 when y = 0 and x = 1.
2.dx/dt = g(1- e^-kt)/k , express x in terms of g,k and t.

2. ## Re: Find particular solution by substitution

Okay, if y= vx, then dy/dx= v+ x dv/dx. What do you get when you replace y by vx and dy/dx by v+ x dv/dx?

The second looks like a straightforward integration.

3. ## Re: Find particular solution by substitution

Are g and k constants?

4. ## Re: Find particular solution by substitution

Originally Posted by Prove It
Are g and k constants?
Yes

Originally Posted by HallsofIvy
Okay, if y= vx, then dy/dx= v+ x dv/dx. What do you get when you replace y by vx and dy/dx by v+ x dv/dx?

The second looks like a straightforward integration.
I got dv/dx = (x+v-vx-xv^2)/(x^2 + vx^2), what's next? How can I solve this?
The second is exactly the straightforward integration, but I'm not able to solve it.......Some guide, please?