Internal problem ID [13865]
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: 28.6 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+7 y=165 \,{\mathrm e}^{4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 8, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 4.906 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+8*diff(y(t),t)+7*y(t)=165*exp(4*t),y(0) = 8, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \left (3 \,{\mathrm e}^{11 t}+4 \,{\mathrm e}^{6 t}+1\right ) {\mathrm e}^{-7 t} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 25
DSolve[{y''[t]+8*y'[t]+7*y[t]==165*Exp[4*t],{y[0]==8,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-7 t}+4 e^{-t}+3 e^{4 t} \]