Internal problem ID [14520]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=-{\mathrm e}^{-9 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=-exp(-9*t),y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-9 t} \left ({\mathrm e}^{10 t} c_{1} +c_{2} {\mathrm e}^{12 t}-\frac {1}{120}\right ) \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 29
DSolve[y''[t]-4*y'[t]+3*y[t]==-Exp[-9*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {e^{-9 t}}{120}+c_1 e^t+c_2 e^{3 t} \]