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The solution of $\cos y \frac{d y}{d x}=e^{x+\sin y}+x^2 e^{\sin y}$ is $f(x)+e^{-\sin y}=C$ (C is arbitrary real constant) where $f(x)$ is equal to
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The correct answer is:
$e^x+\frac{1}{3} x^3$
$-e^{-\sin y} \cos y \frac{d y}{d x}=-\left[e^x+x^2\right] \Rightarrow d\left(e^{-\sin y}\right)+\left(e^x+x^2\right) d x=0 \Rightarrow e^{-\sin y}+e^x+\frac{x^3}{3}=C$
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