Internal problem ID [4943]
Book: ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG,
EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section: Chapter 6. Laplace Transforms. Problem set 6.3, page 224
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+10 y^{\prime }+24 y-144 t^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {19}{12}}, y^{\prime }\relax (0) = -5\right ] \end {align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 14
dsolve([diff(y(t),t$2)+10*diff(y(t),t)+24*y(t)=144*t^2,y(0) = 19/12, D(y)(0) = -5],y(t), singsol=all)
\[ y \relax (t ) = 6 t^{2}-5 t +\frac {19}{12} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[{y''[t]+10*y'[t]+24*y[t]==144*t^2,{y[0]==19/12,y'[0]==-5}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to t (6 t-5)+\frac {19}{12} \\ \end{align*}