Internal problem ID [14531]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(t),t$2)+diff(y(t),t)-2*y(t)=-1,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (2 c_{2} {\mathrm e}^{3 t}+{\mathrm e}^{2 t}+2 c_{1} \right ) {\mathrm e}^{-2 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 23
DSolve[y''[t]+y'[t]-2*y[t]==-1,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 e^{-2 t}+c_2 e^t+\frac {1}{2} \]