Internal problem ID [14845]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-8 y=-t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(t),t$2)-2*diff(y(t),t)-8*y(t)=-t,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{4 t} c_{2} +{\mathrm e}^{-2 t} c_{1} +\frac {t}{8}-\frac {1}{32} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 30
DSolve[y''[t]-2*y'[t]-8*y[t]==-t,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t}{8}+c_1 e^{-2 t}+c_2 e^{4 t}-\frac {1}{32} \]