Internal problem ID [13871]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number: 28.9 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+40 y=122 \,{\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 5.25 (sec). Leaf size: 29
dsolve([diff(y(t),t$2)-4*diff(y(t),t)+40*y(t)=122*exp(-3*t),y(0) = 0, D(y)(0) = 8],y(t), singsol=all)
\[ y \left (t \right ) = -2 \left (-1+\left (\cos \left (6 t \right )-\frac {3 \sin \left (6 t \right )}{2}\right ) {\mathrm e}^{5 t}\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 35
DSolve[{y''[t]-4*y'[t]+40*y[t]==122*Exp[-3*t],{y[0]==0,y'[0]==8}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (3 e^{5 t} \sin (6 t)-2 e^{5 t} \cos (6 t)+2\right ) \]