1.
\(y'' - 2y' - 3y = 24 e^{-3t}\text{,}\) \(y(0) = 1\text{,}\) \(y'(0) = 0\)
2.
\(y'' - y' - 2y = 4x^2\text{,}\) \(y(0) = -1\text{,}\) \(y'(0) = 1\)
3.
\(\dfrac{d^2x}{dx^2} - 6 \dfrac{dx}{dt} + 25 x = 64e^{-t}\text{,}\) \(x(0) = 1\text{,}\) \(x'(0) = -2\)
4.
\(y'' + 16y = 2 \sin 2t\text{,}\) \(y(0) = 1\text{,}\) \(y'(0) = 0\)
5.
\(y'' + 16y = 2 \sin 4t\text{,}\) \(y(0) = 1\text{,}\) \(y'(0) = 0\)
6.
\(y'' + 2y' + y = 2e^{-t}\text{,}\) \(y(0) = -1\text{,}\) \(y'(0) = 3\)
7.
\(y'' + 6y' + 8y = \cos 3t\text{,}\) \(y(0) = -2\text{,}\) \(y'(0) = 1\)
8.
\(u'' + \omega_0^2 y = \cos \omega t\text{,}\) \(\omega^2 \neq \omega_0^2\text{,}\) \(u(0) = 1\text{,}\) \(u'(0) = -1\)