## Solution of Linear Differential equations

__Solution of Linear Differential equations:__

One of the important applications of Laplace transforms is to solve linear differential equations with constant coefficients with initial conditions. For example, consider a second order linear differential equations:

Taking Laplace transforms on both sides of the above equation and using the formulae on Laplace transforms of the derivatives *y*′ and *y*′′. We recall the formulae for immediate reference.

**and so on.
**

**Example:**

**(1) Solve using Laplace Transform.**

**Solution:** Given equation is y'' - 3y' 2y = e^{3t}

Where y (0) = 0 and y' (0) =0

Hence this is the required solutions.