87.11.17 problem 17

Internal problem ID [23435]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 84
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:41:43 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-4 y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=2*diff(diff(y(x),x),x)-4*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{x \sqrt {6}}+c_2 \right ) {\mathrm e}^{-\frac {\left (-2+\sqrt {6}\right ) x}{2}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 35

ode=2*D[y[x],{x,2}]-4*D[y[x],x]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{x-\sqrt {\frac {3}{2}} x} \left (c_2 e^{\sqrt {6} x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 4*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x \left (1 - \frac {\sqrt {6}}{2}\right )} + C_{2} e^{x \left (1 + \frac {\sqrt {6}}{2}\right )} \]