Internal problem ID [14522]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y=-4+2 t} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(t),t$2)-y(t)=2*t-4,y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-t}+{\mathrm e}^{t} c_{1} -2 t +4 \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 24
DSolve[y''[t]-y[t]==2*t-4,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -2 t+c_1 e^t+c_2 e^{-t}+4 \]