Internal problem ID [5685]
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]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+12 y=21 \,{\mathrm e}^{3 t}} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {7}{2}}, y^{\prime }\left (0\right ) = -10\right ] \end {align*}
✓ Solution by Maple
Time used: 0.797 (sec). Leaf size: 15
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)
\[ y \left (t \right ) = \frac {5 \,{\mathrm e}^{-4 t}}{2}+\cosh \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.019 (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]
\[ y(t)\to \frac {1}{10} e^{-4 t} \left (155 e^t+5 e^{7 t}-128\right ) \]