Question

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

Answer 1

Where are you stuck?

Answer 2

okay i separated them by using separation of intervals, then i dont know if i should integration by parts next

Answer 3

use integration by parts on \[\int\ln(t)dt\]

Answer 4

not on cos?

Answer 5

when you separate you will have \(\int\sec^2(y)dy\)

Answer 6

you don't need parts for that

Answer 7

okay i chose my u,du,v, and dv and got\[lnt(t)-\int\limits(t)\frac{ 1 }{ t}dt\]

Answer 8

ok...provided your lnt(t) is \(\ln(t)\cdot t\)

Answer 9

okay do i know take the antiderivative of the integral which will be ln(t) dt?