Internal problem ID [4658]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page
95
Problem number: Problem 11.4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+25 y-2 \sin \left (\frac {t}{2}\right )+\cos \left (\frac {t}{2}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 37
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+25*y(t)=2*sin(t/2)-cos(t/2),y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{3 t} \sin \left (4 t \right ) c_{2}+{\mathrm e}^{3 t} \cos \left (4 t \right ) c_{1}+\frac {56 \sin \left (\frac {t}{2}\right )}{663}-\frac {20 \cos \left (\frac {t}{2}\right )}{663} \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 48
DSolve[y''[t]-6*y'[t]+25*y[t]==2*Sin[t/2]-Cos[t/2],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{663} \left (56 \sin \left (\frac {t}{2}\right )-20 \cos \left (\frac {t}{2}\right )\right )+e^{3 t} (c_2 \cos (4 t)+c_1 \sin (4 t)) \\ \end{align*}