Chapter D2.1, Problem 54E

a.

To determine

To verify: The functions $y=\sin t\text{ and }y=\cos t$ are solutions of the given differential equation.

b.

To determine

To write: The general solution of the differential equation $y^{″}+y=0$.

c.

To determine

To verify: The function $y=\sin 2t\text{ and }y=\cos 2t$ is a solution of the given differential equation.

d.

To determine

To write: The general solution of the differential equation $y^{″}+4y=0$.

e.

To determine

To find: The general solution of the differential equation $y^{″}+k^{2}y=0$.