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Question
Find the general solution of the following differential equation:
`(dy)/(dx) = e^(x-y) + x^2e^-y`
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Solution
Given differential equation is `(dy)/(dx) = e^(x-y) + x^2e^-y`
⇒ `(dy)/(dx) = e^-y(e^x + x^2)`
⇒ `(dy)/e^-y = dx(e^x + x^2)`
⇒ `e^ydy = e^xdx + x^2dx`
On integrating both sides, we get
`e^y = e^x + x^3/3 + c`
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