Internal problem ID [11010]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }-7 y-4=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(t),t$2)-3*diff(y(t),t)-7*y(t)=4,y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{\frac {\left (3+\sqrt {37}\right ) t}{2}} c_{2} +{\mathrm e}^{-\frac {\left (-3+\sqrt {37}\right ) t}{2}} c_{1} -\frac {4}{7} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 39
DSolve[y''[t]-3*y'[t]-7*y[t]==4,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {4}{7}+e^{-\frac {1}{2} \left (\sqrt {37}-3\right ) t} \left (c_2 e^{\sqrt {37} t}+c_1\right ) \\ \end{align*}