# S6.

Solution:

Let’s execute the Laplace transformation both side of the equation!

Let’s substitute the available initial conditions

Result of the inverse Laplace transformation will give , as the general solution:

First step is to find the roots of denominator:

One real root of the third order polynomial is , which means the polynomial can be expressed by fully-factored form as follow

Next task is to determine the coefficients of the partial function

Solution of this equation will give the coefficients.

Let’s see the following cases:

If will be substituted, then can be obtained.

Consequently, the solution is