Internal problem ID [14544]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-20 y=-2 \,{\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(t),t$2)-diff(y(t),t)-20*y(t)=-2*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (10 c_{2} {\mathrm e}^{9 t}+{\mathrm e}^{5 t}+10 c_{1} \right ) {\mathrm e}^{-4 t}}{10} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 29
DSolve[y''[t]-y'[t]-20*y[t]==-2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^t}{10}+c_1 e^{-4 t}+c_2 e^{5 t} \]