Chapter 16, Problem 57RE

a)

To determine

How, by observing you know that a form of a particular solution of the differential equation $y\text{'}\text{'}+3y=12\sin x$ is $y_p=A\sin x$.

b)

To determine

To calculate: Using the explanation in part (a) find a particular solution of the differential equation $y\text{'}\text{'}+5y=10\cos x$.

c)

To determine

Compare the algebra required to find the particular solutions in parts (a) and (b) with that required when the form of the particular solution is $y_p=A\cos x+B\sin x$.