I need help completing this problem:(adsbygoogle = window.adsbygoogle || []).push({});

y'' - 4k^2 y^2 = 0, y(0) = 2, y'(0) = 4k, k > 0 and fixed constant

Let v = y'

dv/dx = dv/dy * dy/dx = dv/dy * v

dv/dy * v - 3k^2 y^2 = 0

Integral( v dv ) = Integral( 3k^2 y^2 )

v^2 = 2k^2 y^3 + C0

v(0) = 4k ==> C0 = 16k^2

dy/dx = sqrt( 2k^2 y^3 + 16k^2 )

I think this is separable, but I can't do the integral, so I think I messed up somewhere.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help Finishing ODE

**Physics Forums | Science Articles, Homework Help, Discussion**