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