Internal problem ID [14521]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=2 \,{\mathrm e}^{3 t}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(t),t$2)-4*diff(y(t),t)+3*y(t)=2*exp(3*t),y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{2} +t \right ) {\mathrm e}^{3 t}+{\mathrm e}^{t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 25
DSolve[y''[t]-4*y'[t]+3*y[t]==2*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to c_1 e^t+e^{3 t} \left (t-\frac {1}{2}+c_2\right ) \]