Question

Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.

Answer 1

Find general solution of the non-homogeneous equation.

y''+4y=3sec^2(2t)

First solve the homogeneous equation:

y''+4y=0

r^2+4=0

r_{1}=+2i and r_{2}=-2i

So therefore, the general solution of the homogeneous part is:

y(t)=C_{1}cos2t+C_{2}sin2t

Now we must solve for the non-homogencous part:

So therefore the final solution is: