67.5.8 problem Problem 2(c)

Internal problem ID [14094]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 6. Introduction to Systems of ODEs. Problems page 408
Problem number : Problem 2(c)
Date solved : Tuesday, January 28, 2025 at 06:14:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }-7 y&=4 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(t),t$2)-3*diff(y(t),t)-7*y(t)=4,y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {\left (3+\sqrt {37}\right ) t}{2}} c_{2} +{\mathrm e}^{-\frac {\left (-3+\sqrt {37}\right ) t}{2}} c_{1} -\frac {4}{7} \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 43

DSolve[D[y[t],{t,2}]-3*D[y[t],t]-7*y[t]==4,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 e^{-\frac {1}{2} \left (\sqrt {37}-3\right ) t}+c_2 e^{\frac {1}{2} \left (3+\sqrt {37}\right ) t}-\frac {4}{7} \]