## Solution of Non-homogenous Linear Differential Equation

**Solution of Non-homogenous Linear Differential Equation**

**Specific forms of the Particular integral**

## Topics

Differential equations of second and higher order with constant coefficients

Solution of Homogeneous Linear Differential equation

Solution of Non-homogenous Linear Differential Equation

## Homogeneous Linear Differential equation problems

- Solve (d^3/dx^3)y-2(d^2/dx^2)y+4(d/dx)y-8y=0
- Solve (d^3/dx^3)y+6(d^2/dx^2)y+11(d/dx)y+6y=0
- Solve (4D^4-4D^3-23D^2+12D+36)y=0
- Solve (d^4/dx^4)y + 8 (d^2/dx^2)y+16y=0

## Non-homogeneous Linear Differential equation problems

- Solve (d^2/dt^2)x-6(dx/dt)+9x=5e^(-2t)
- Solve (d^2/dx^2)y-4y=cosh(2x-1)+3^x
- Solve (D^4-18D^2+81)y=36 e^(3x)
- Solve (D^2-1)y = 3x^2+6x+12
- Solve d^2y/dx^2 -6dy/dx+25y = e^2x +sin x + x
- Solve (d^4y/dt^4)-y = e^t cos t
- Solve y’’-y = x^2 cos x
- Solve d^2 y/dx^2 -y = (1+x^2)e^x +x sin x