74.11.3 problem 15

Internal problem ID [16253]
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
Date solved : Tuesday, January 28, 2025 at 08:58:45 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=2 \,{\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \left (c_{2} +t \right ) {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 25

DSolve[D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==2*Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^t+e^{3 t} \left (t-\frac {1}{2}+c_2\right ) \]