Question

By using integration by parts. Solve the solution for the following DE.
y'=(cos^(2)y)ln(t)

Answer 1

Separation of variables gives us:\[\Large\rm \frac{dy}{\cos^2y}=\ln t ~dt\]So we need to integrate some stuff,\[\Large\rm \int\limits \sec^2y~dy=\int\limits \ln t ~dt\]Where you having trouble? With integrating the log?

Answer 2

By parts:\[\Large\rm u=\ln t, \qquad\qquad dv=dt\]\[\Large\rm du=\frac{1}{t}dt, \qquad \quad v=t\]

Answer 3

I'll bet you can figure it out from there cash mony :O

Answer 4

so is separation by parts the second step to solving the first step which was separation by variables?

Answer 5

@zepdrix