Legendre Linear Equation
Legendre Linear Equation:
It is the Form:
Where A1,A2,..........,An are constants. It can be reduced to linear differential equation with constant coefficients.
Substitue (2) in (1) gives: the linear differential equation of constant coefficients.
Examples: Solve (2x 3)2y'' - (2x 3)y' - 12y = 6x
Solution: This is Legendre's linear equation:
(2x 3)2y'' - (2x 3)y' - 12y = 6x................(1)
Put z = log (2x 3), ez = 2x 3
(2x 3)D = 2θ