Solving Linear Differential Equations

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