# Solution of y” + 3y’ + 2y = 4sin(x) – 6cos(x).

(1)

By solving left hand side,

(2)

(3)

Solving for , we get:

(4)

Thus, the complementary function is:

(5)

To find the particular solution, we use the method of undetermined coefficients. Since the right-hand side of the given differential equation is of the form , we assume a particular solution of the form:

(6)

(7)

(8)

Simplifying this equation, we get:

(9)

Equating the coefficients of and on both sides of the equation, we get:

(10)

Solving for and , we get:

(11)

Thus, the particular solution is:

(12)

The general solution is:

(13)
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