74.12.3 problem 3

Internal problem ID [16310]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 09:02:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+10 y&={\mathrm e}^{3 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(diff(y(t),t$2)-7*diff(y(t),t)+10*y(t)=exp(3*t),y(t), singsol=all)
 

\[ y = c_{2} {\mathrm e}^{5 t}+c_{1} {\mathrm e}^{2 t}-\frac {{\mathrm e}^{3 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 31

DSolve[D[y[t],{t,2}]-7*D[y[t],t]+10*y[t]==Exp[3*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {e^{3 t}}{2}+c_1 e^{2 t}+c_2 e^{5 t} \]