Internal problem ID [4939]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }+5 y-50 t +100=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = -4, y^{\prime }\relax (2) = 14] \end {align*}
✓ Solution by Maple
Time used: 0.039 (sec). Leaf size: 37
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+5*y(t)=50*t-100,y(2) = -4, D(y)(2) = 14],y(t), singsol=all)
\[ y \relax (t ) = 2 \sin \left (2 t \right ) \cos \relax (4) {\mathrm e}^{-t +2}-2 \cos \left (2 t \right ) \sin \relax (4) {\mathrm e}^{-t +2}+10 t -24 \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[{y''[t]+2*y'[t]+5*y[t]==50*t-100,{y[2]==-4,y'[2]==14}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 10 t-2 e^{2-t} \sin (4-2 t)-24 \\ \end{align*}