81.15.9 problem 19-10

Internal problem ID [21717]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 19. Change of variables. Page 483
Problem number : 19-10
Date solved : Thursday, October 02, 2025 at 08:01:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+\left (1-\frac {2}{\left (1+3 x \right )^{2}}\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 43

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+(1-2/(3*x+1)^2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \sqrt {1+3 x}\, \left (\left (1+3 x \right )^{-\frac {\sqrt {17}}{6}} c_2 +\left (1+3 x \right )^{\frac {\sqrt {17}}{6}} c_1 \right ) \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 70

ode=D[y[x],{x,2}]+2*D[y[x],x]+(1- 2/(1+3*x)^2)*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-x} (6 x+2)^{\frac {1}{6} \left (3-\sqrt {17}\right )}+\frac {c_2 e^{-x} \sqrt {3 x+1} (6 x+2)^{\frac {\sqrt {17}}{6}}}{\sqrt {34}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - 2/(3*x + 1)**2)*y(x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False