In 11–18, find a general solution to the differential equation.

Solution:Step 1In this problem we need to find a general solution to the given differential equation.Step 2Given : The auxiliary equation to find the complementary solution of the given differential equation is .To solve the auxiliary equation, we do as followsWe know that if the roots of the auxiliary equation has complex roots , then The general solution for the problem can be written as :Here the roots are with and therefore the solution for the problem is Step 3We will use the method of variation of parameters.Now we will find the particular solution for .Here we have and . Also we know...