63.1.9 problem 9

Internal problem ID [13033]
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
Date solved : Tuesday, January 28, 2025 at 04:49:48 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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: 0.019 (sec). Leaf size: 24

DSolve[2*D[x[t],{t,2}]-5*D[x[t],t]-3*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_1 e^{-t/2}+c_2 e^{3 t} \]