Internal problem ID [14851]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=-4 \,{\mathrm e}^{-2 t}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=-4*exp(-2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (3 c_{1} {\mathrm e}^{4 t}+3 c_{2} {\mathrm e}^{3 t}-1\right ) {\mathrm e}^{-2 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 29
DSolve[y''[t]-3*y'[t]+2*y[t]==-4*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {e^{-2 t}}{3}+c_1 e^t+c_2 e^{2 t} \]