Internal problem ID [4932]
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: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+7 y^{\prime }+12 y-21 \,{\mathrm e}^{3 t}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = {\frac {7}{2}}, y^{\prime }\relax (0) = -10\right ] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+7*diff(y(t),t)+12*y(t)=21*exp(3*t),y(0) = 7/2, D(y)(0) = -10],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left ({\mathrm e}^{7 t}+{\mathrm e}^{t}+5\right ) {\mathrm e}^{-4 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 28
DSolve[{y''[t]+7*y'[t]+12*y[t]==21*Exp[3*t],{y[0]==32/10,y'[0]==62/10}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{10} e^{-4 t} \left (5 e^t \left (e^{6 t}+31\right )-128\right ) \\ \end{align*}