Toronto Math Forum

MAT244-2013S => MAT244 Math--Tests => Final Exam => Topic started by: Victor Ivrii on April 17, 2013, 02:59:06 PM

Title: FE-1
Post 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 $y(0) = 1$.
Title: Re: FE-1
Post by: Jason Hamilton on April 17, 2013, 04:22:46 PM
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
Title: Re: FE-1
Post by: Victor Lam on April 17, 2013, 06:07:07 PM
solution
Title: Q1
Post by: Benny Ho on April 17, 2013, 09:18:39 PM
Solution