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Question
Solve the differential equation:
`e^(dy/dx) = x`
Solution
`e^(dy/dx) = x`
∴ `dy/dx = log x`
∴ dy = log x dx
Integrating on both sides, we get
`int dy = int (logx)1 dx`
∴ `y = log x int1dx - int [ d/dx(logx)int1dx] dx`
= `x log x -int 1/x. x dx`
= `x log x -int dx`
∴ y = x log x - x + c
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