74.11.14 problem 26

Internal problem ID [16264]
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 : 26
Date solved : Tuesday, January 28, 2025 at 08:59:23 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime }+y^{\prime }-4 y&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(5*diff(y(t),t$2)+diff(y(t),t)-4*y(t)=-3,y(t), singsol=all)
 

\[ y = \frac {\left (4 \,{\mathrm e}^{\frac {9 t}{5}} c_{1} +3 \,{\mathrm e}^{t}+4 c_{2} \right ) {\mathrm e}^{-t}}{4} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 27

DSolve[5*D[y[t],{t,2}]+D[y[t],t]-4*y[t]==-3,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{4 t/5}+c_2 e^{-t}+\frac {3}{4} \]