For the solution to the differential equation y 3 y 10 si

For the solution to the differential equation y \' - 3 y = 10 sin t What is the coefficient of the term involving sin t ?

Solution

Let particular solution be:

yp= A sin(t)+B cos(t)

Substituting gives

A cos(t)-B sin(t)-3(A sin(t)+B cos(t))=10 sin(t)

A-3B=0---------------->A=3B

-B-3A=10

Hence, B=1, A=3

So coefficient of sin(t) is 3