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Question
Solve the following differential equation.
`dy/dx + y = e ^-x`
Solution
`dy/dx + y = e ^-x`
The given equation is of the form
`dy/dx + py = Q`
where, P = 1 and Q = e-x
∴ I.F. = `e int ^(pdx) = e int ^(1.dx)= e^x`
∴ Solution of the given equation is
`y (I.F.) = int Q (I.F.) dx + c`
∴ `y e^x = int e^-x e ^xdx+c`
∴ `y e^x = int 1dx +c`
∴ y ex = x+c
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