1.

The solution of differential equation `(dy)/(dx)=e^(x-y)+x^(2)e^(-y)`isA. `y=e^(x-y)-x^(2)e^(-y)+C`B. `e^(y)-e^(x)=(x^(3))/(3)+C`C. `e^(x)+e^(y)=(x^(3))/(3)+C`D. `e^(x)-e^(y)=(x^(3))/(3)+C`

Answer» Given that, `(dy)/(dx)=e^(x-y)+x^(2)e^(-y)`
`Rightarrow (dy)/(dx)=e^(x)e^(-y)+x^(2)e^(-y)`
`Rightarrow (dy)/(dx)=(ex^(2)+x^(2))/(e^(y))`
On integrating both sides, we get
`inte^(y) dy=int(e^(x)+x^(2))dx`
`Rightarrow e^(y)=e^(x)+(x^(3))/(3)+C``Rightarrow e^(y)-e^(x)=(x^(3))/(3)+C`


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