# Non-linear differential equation

by pd1zz13
Tags: differential, equation, nonlinear
 P: 1,666 That's a common way to do it and you're left with: $$u^2=4k\sqrt{v}+c$$ or: $$\left(\frac{dv}{dt}\right)^2=4k\sqrt{v}+c$$ taking square roots, separate variable again and get: $$\frac{dv}{\sqrt{4k\sqrt{v}+c}}=\pm dt$$ That however looks kinda' messy to integrate although Mathematica gives a nice expression for the left side but then you get an implicit expression for v in terms of t: $$g(v)=\pm(t+c_2)$$ which is not solvable explicitly for v(t). Doesn't look like it anyway.