67.2.25 problem Problem 3(c)

Internal problem ID [13982]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 3(c)
Date solved : Tuesday, January 28, 2025 at 06:10:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(2*diff(y(x),x$2)-3*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x} c_{1} +{\mathrm e}^{-\frac {x}{2}} c_{2} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

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

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