For the following sets of parameters, find the homogeneous solution \(y_h\) for eq. ¿eq:ioode? with the order \(n\) and coefficients \(a_i\) given.

1. \(n = 2\), \(a_1 = -1\), \(a_0 = -2\)
2. \(n = 2\), \(a_1 = 6\), \(a_0 = 9\)
3. \(n = 2\), \(a_1 = 10\), \(a_0 = 34\)
4. \(n = 5\), \(a_4 = -7\), \(a_3 = 32\), \(a_2 = -124\), \(a_1 = 256\), \(a_0 = -192\)

For the following sets of parameters, find the particular solution \(y_p\) for eq. ¿eq:ioode? with the order \(n\), coefficients \(a_i\), and forcing function \(f\) given.

1. \(n = 2\), \(a_1 = -1\), \(a_0 = -2\), \(f(t) = 3\)
2. \(n = 2\), \(a_1 = 6\), \(a_0 = 9\), \(f(t) = 5 e^{-3 t}\)
3. \(n = 1\), \(a_0 = 2\), \(f(t) = 2 \cos(3 t)\)
4. \(n = 3\), \(a_2 = 5\), \(a_1 = 16\), \(a_0 = 80\), \(f(t) = t+2\)

For the following sets of parameters, find the specific solution \(y\) for eq. ¿eq:ioode? with the order \(n\), coefficients \(a_i\), forcing function \(f\), and initial conditions given.
Note that the homogeneous and particular solutions from problem 7.2 apply to these problems, so they need not be re-derived.

1. \(n = 2\), \(a_1 = -1\), \(a_0 = -2\), \(f(t) = 3\), \(y(0) = 2\), \(d y/d t|_{t=0} = 0\)
2. \(n = 2\), \(a_1 = 6\), \(a_0 = 9\), \(f(t) = 5 e^{-3 t}\), \(y(0) = 0\), \(d y/d t|_{t=0} = 0\)
3. \(n = 1\), \(a_0 = 2\), \(f(t) = 2 \cos(3 t)\), \(y(0) = 4\)
4. \(n = 3\), \(a_2 = 5\), \(a_1 = 16\), \(a_0 = 80\), \(f(t) = t+2\), \(y(0) = 0\), \(d y/d t|_{t=0} = 1\), \(d^2 y/d t^2|_{t=0} = 0\)