Sunday, November 16, 2008

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

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