Internal problem ID [10339]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.1 First order equations. Exercises page
10
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {2 x^{\prime \prime }-5 x^{\prime }-3 x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(2*diff(x(t),t$2)-5*diff(x(t),t)-3*x(t)=0,x(t), singsol=all)
\[ x \left (t \right ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-\frac {t}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[2*x''[t]-5*x'[t]-3*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{-t/2}+c_2 e^{3 t} \\ \end{align*}