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kow [346]
1 year ago
5

Using separation of variables technique, solve the following differential equation with initial condition y'= e sinx and y(pi) =

0. The solution is: ​

Mathematics
1 answer:
inessss [21]1 year ago
3 0

\begin{aligned}&y'=e^y\sin x\\&\dfrac{dy}{dx}=e^y\sin x\\&\dfrac{dy}{e^y}=\sin x\, dx\\&\int \dfrac{dy}{e^y}=\int \sin x\, dx\\&-e^{-y}=-\cos x+C\\&e^{-y}=\cos x+C\\\end

e^{-0}=\cos \pi +C\\1=1+C\\C=0\\\\\boxed{\boxed{e^{-y}=\cos x}}

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