67.2.25 problem Problem 3(c)

Internal problem ID [13911]
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 : Monday, March 31, 2025 at 08:17:50 AM
CAS classification : [[_2nd_order, _missing_x]]

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

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

ode:=2*diff(diff(y(x),x),x)-3*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{2 x}+c_2 \,{\mathrm e}^{-\frac {x}{2}} \]

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

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

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

✓ Sympy. Time used: 0.147 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - 3*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {x}{2}} + C_{2} e^{2 x} \]