Problems On Special Form Of X In Differential Equation

Problems on Special Form of X in Differential Equation:

Type:1

1. Solve

Solution: We have ( D² - 5D 6) y = e^5x

               A.E is m2 - 5m 6 = 0

              i.e (m - 2) (m - 3) = 0

              ⇒ m = 2,3

Hence the complementary function is;

∴ C.F = c₁ e^2x c₂ e^3x

Particular Integral (P.I) is; 

∴ The general solution is given by: y = C.F P.I

2. Solve

Solution: We have ( D² - 3D 2)y = 10 e^3x

               A.E is m² - 3m 2 = 0

               i.e (m - 2) (m - 1) = 0

               m = 2,1

∴ The general solution is y = C.F P.I