Toronto Math Forum
MAT244-2013S => MAT244 Math--Tests => Final Exam => Topic started by: Victor Ivrii on April 17, 2013, 02:59:06 PM
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Find the general solution of the differential equation
\begin{equation*}
y' +y \tan x =\sin (x)
\end{equation*}
and solve the initial value problem $y(0) = 1$.
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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
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solution
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Solution