Differential Equations

Question

Find the general solution to the differential equation dy/dx = yln(y).

Answer 1

dy/dx = y lny

1 / (y lny) dy = dx

∫ [ 1 / (y lny) ] dy = ∫ dx

Let u = lny. Then du = (1/y)dy.

So, ∫ (1/u)du = ∫dx

ln u = x + K

ln(lny) = x + K

lny = e^{x + K}

lny = e^Ke^x Let C = e^K, so lny = Ce^x.

Answer 2

Separable equation.

Separate y and x: dy / (y lny) = dx

Integrate both sides and don't forget the integration constant.