In a Linear Differential Equation y and dy/dx appear only in first degree.
The general form is:
dy/dx +Py = Q
P and Q can be functions of x (even constants)
We use integrating factor e∫Pdx.
Multiplying both sides with the integrating factor
e∫Pdx[dy/dx +Py] = Qe∫Pdx
L.H.S. is equal to d/dx of [ye∫Pdx]
d/dx of [ye∫Pdx] = Qe∫Pdx
Integrating both sides w.r.t. x
We get ye∫Pdx = ∫Qe∫Pdx + C