15.9.10 problem 24

Internal problem ID [3067]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 24
Date solved : Tuesday, March 04, 2025 at 03:58:13 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

\[ y = c_{1} {\mathrm e}^{\frac {\left (\sqrt {3}-1\right ) x}{2}}+c_2 \,{\mathrm e}^{-\frac {\left (1+\sqrt {3}\right ) x}{2}} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 35

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

\[ y(x)\to e^{-\frac {1}{2} \left (1+\sqrt {3}\right ) x} \left (c_2 e^{\sqrt {3} x}+c_1\right ) \]

✓ Sympy. Time used: 0.174 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (-1 + \sqrt {3}\right )}{2}} + C_{2} e^{- \frac {x \left (1 + \sqrt {3}\right )}{2}} \]