Toronto Math Forum
MAT2442013S => MAT244 MathTests => Final Exam => Topic started by: Victor Ivrii on April 17, 2013, 02:59:06 PM

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

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

solution

Solution