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.

Printable View

- Mar 26th 2013, 08:41 AMalexander9408Find 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 AMHallsofIvyRe: 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 PMProve ItRe: Find particular solution by substitution
Are g and k constants?

- Mar 27th 2013, 06:30 AMalexander9408Re: Find particular solution by substitution