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Question Number 124923 by bemath last updated on 07/Dec/20

$$\frac{dy}{dx}-y=3\cot x.e^{\sin x}$$$$$$

Commented by mohammad17 last updated on 07/Dec/20

$$P\left(x\right)=-1,Q\left(x\right)=3cotx.e^{sinx}$$$$$$$$(I.f)=e^{\int P\left(x\right)dx}=e^{\int -dx}=e^{-x}$$$$$$$${ye}^{-x}=\int (I.f)Q\left(x\right)dx$$$$$$$${ye}^{-x}=3\int cotx.e^{sinx-1}dx$$$$$$$${ye}^{-x}=\frac{1}{e}Ei\left(sinx\right)+C$$$$$$$$y=e^{x-1}Ei\left(sinx\right)+{Ce}^x$$$$$$$$(MohammadAl-dolaimy)$$

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