# Find particular solution by substitution

• Mar 26th 2013, 08:41 AM
alexander9408
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.
• Mar 26th 2013, 10:06 AM
HallsofIvy
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.
• Mar 26th 2013, 05:23 PM
Prove It
Re: Find particular solution by substitution
Are g and k constants?
• Mar 27th 2013, 06:30 AM
alexander9408
Re: Find particular solution by substitution
Quote:

Originally Posted by Prove It
Are g and k constants?

Yes

Quote:

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?