Question

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

Answer 1

Are you sure it is "Integration by Parts" and not "Separation of Variables"?

\(\dfrac{dy}{\cos^{2}(y)} = ln(t)\;dt\)

\(\sec^{2}(y)\;dy = ln(t)\;dt\)

Well, okay, the right hand side will still take Integration by parts.

Answer 2

is the right hand side this \[tln(t)-\int\limits(t)\frac{ 1 }{ t}dt\]

Answer 3

Looks good to me. Why do you doubt?

Answer 4

What did you get for the left side?

Answer 5

tan(y)=tln(t)-t+c