Get the answer to "cos⁡x(e2y−y)dydx=eysin⁡2x,y(0)=0"

Reeves

Answered question

2020-11-08

\cos x (e^{2 y} - y) \frac{d y}{d x} = e^{y} \sin 2 x, y (0) = 0

hosentak

Skilled2020-11-09Added 100 answers

On separating the variables,

\frac{e^{2 y} - y}{e^{y}} d y = \frac{2 \sin s \cos x}{\cos x} d x

(e^{y} - y e^{- y}) d y = 2 \sin x d x

integrating both sides,

e^{y} + (y + 1) e^{- y} = - 2 \cos x + C

since y(0) = 0
then 1+(0+1)(1)=-2+C
that is C=4
then

e^{y} + (y + 1) e^{- y} = - 2 \cos x + 4

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