Chapter D2.2, Problem 39E

a.

To determine

Whether the statement “To solve the equation $y^{″}+t{y}^{\prime }+4y=0$ you should use the trial solution $y=e^{rt}$” is true or not.

b.

To determine

Whether the statement “The equation $y^{″}+t{y}^{\prime }+4t^{2}y=0$ is a Cauchy-Euler equation” is true or not.

c.

To determine

Whether the statement “A second-order differential equation with constant real coefficients has a characteristic polynomial with roots $2+3i$ and $-2+3i$” is true or not.

d.

To determine

Whether the statement “The general solution of a second-order homogeneous differential equation with constant real coefficients could be $y=c_1\cos 2t+c_2\sin t\cos t$” is true or not.

e.

To determine

Whether the statement “The general solution of a second-order homogeneous differential equation with constant real coefficients could be $y=c_1\cos 2t+c_2\sin 3t$” is true or not.