Linear Differential equation of second order with constant coefficients

The general form of the linear differential equation of second order is
d2y/dx2 + P dy/dx + Qy = R
where P and Q are constants and R is a function of x or constant.

Differential Operator

Symbol D stands for the operation of differential i.e.
Dy = dy/dx
D2y = d2y/dx2

1/D stands for the operation of integration.
1/D2 stands for the operation of integration twice.

d2y/dx2 + P dy/dx + Qy = R can be written in the operator form
D2y + P Dy + Qy = R or (D2 + PD + Q)y = R


Complete Solution = Complementary function + Particular Integral



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