FE-1

[Victor Ivrii]

Find the general solution of the differential equation
\begin{equation*}
y' +y \tan x =\sin (x)
\end{equation*}
and solve the initial value problem $y(0) = 1$.

[Jason Hamilton]

find integrating factor: u=exp(integral tanxdx)=sec x


secx y= integral (tan x)= - ln (cosx) +C

y=-cosx(ln cosx) + C cosx

y(0)=1 => C=1

y=-cosx(ln cosx) + cosx

[Victor Lam]

solution

[Benny Ho]

Solution