Internal problem ID [4931]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.2, page 216
Problem number: 6.
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 }+5 y-29 \cos \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {16}{5}}, y^{\prime }\relax (0) = {\frac {31}{5}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(t),t$2)-6*diff(y(t),t)+5*y(t)=29*cos(2*t),y(0) = 16/5, D(y)(0) = 31/5],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{t}+2 \,{\mathrm e}^{5 t}+\frac {\cos \left (2 t \right )}{5}-\frac {12 \sin \left (2 t \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 31
DSolve[{y''[t]-6*y'[t]+5*y[t]==29*Cos[2*t],{y[0]==32/10,y'[0]==62/10}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t+2 e^{5 t}+\frac {1}{5} (\cos (2 t)-12 \sin (2 t)) \\ \end{align*}