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  • The solution of the differential equation frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} is (a) y=e^{x-y}-x^{2} e^{-y}+c

The solution of the differential equation \frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} is
(a) y=e^{x-y}-x^{2} e^{-y}+c
(b) e^{y}-e^{x}=\frac{x^{3}}{3}+c
(c) e^{x}+e^{y}=\frac{x^{3}}{3}+c
(d) e^{x}-e^{y}=\frac{x^{3}}{3}+c

Answers (1)

The answer is the option (b)  e^{y}-e^{x}=\frac{x^{3}}{3}+c

Explaination:

\\ \frac{d y}{d x}=e^{x-y}+x^{2} e^{-y} \\\\ e^{y} d y=\left(e^{x}+x^{2}\right) d x \\\\ \int e^{y} d y=\int\left(e^{x}+x^{2}\right) d x \\\\ e^{y}=e^{x}+\frac{x^{3}}{3}+C \\\\ e^{y}-e^{x}=\frac{x^{3}}{3}+C

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