Chapter D2.1, Problem 65E

a.

To determine

To verify: The function $y=e^{\frac{-3t}{2}}\left(c_1\sin 2t+c_2\cos 2t\right)$ is a solution of the differential equation $y^{″}+3y^{\prime }+\frac{25}{4}y=0$.

b.

To determine

To find: The solution of the initial value problem $y^{″}+3y^{\prime }+\frac{25}{4}y=0;y\left(0\right)=4,y^{\prime }\left(0\right)=0$.

c.

To determine

To draw: The graph of the function $y=e^{-\frac{3t}{2}}\left(3\sin 2t+4\cos 2t\right)$.