Second Order Linear Differential Equation (Non-constant coefficients)

1. Apr 27, 2013

SherlockOhms

1. The problem statement, all variables and given/known data
Find the general solution for the following differential equation:
y'' + x(y')^2 = 0.

2. Relevant equations
Integration, differentiation...

3. The attempt at a solution
Usually for these sort of DE you could use the substitution v(x) = y'(x) and this would simplify such an equation to a first order DE. The (y')^2 part is throwing me off as this would give the equation:
v(x)' + x(v(x))^2 = 0.
This would be grand if it weren't for the v(x)^2 term. Any ideas on how to get around this? Thanks.

2. Apr 27, 2013

CAF123

Are you worried about the v^2 term because it makes the eqn non-linear? If so, there are ways to solve such an equation.

3. Apr 27, 2013

SherlockOhms

Yeah. We've only covered linear DE's.

4. Apr 27, 2013

CAF123

Are you at all familiar with separation of variables?

5. Apr 27, 2013

SherlockOhms

Yeah. So I'll have v'(x) = (-x)(v(x))^2 and I can then separate the variables and solve. Thanks!