Internal problem ID [4936]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+\frac {9 y}{4}-9 t^{3}-64=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = 1, y^{\prime }\relax (0) = {\frac {63}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 28
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+225/100*y(t)=9*t^3+64,y(0) = 1, D(y)(0) = 63/2],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-\frac {3 t}{2}}+{\mathrm e}^{-\frac {3 t}{2}} t +4 t^{3}-16 t^{2}+32 t \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 27
DSolve[{y''[t]+3*y'[t]+225/100*y[t]==9*t^3+64,{y[0]==1,y'[0]==315/10}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-3 t/2} (t+1)+4 t ((t-4) t+8) \\ \end{align*}