General solution of differential equation XY '+ y = e * XY' + y = e *

xy'＋y＝e^x
First, find the general solution of the homogeneous equation XY '+ y = 0
Separated variables: dy / y = - DX / X
Two side integral: LNY = - LNX + LNC
So y = C / X
Seeking the general solution of nonhomogeneous equation again
Let the general solution of the non-homogeneous equation be y = C (x) / x, and substitute it into the equation to get C '(x) = e ^ x, so C (x) = e ^ x + C
Therefore, y = [e ^ x + C] / x, which is the general solution of the original equation

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