59.1.360 problem 367

Internal problem ID [9532]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 367
Date solved : Sunday, March 30, 2025 at 02:36:57 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: 27

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);
 

\[ y = {\mathrm e}^{-x} \left (1+3 x \right )^{{1}/{3}} \left (\left (1+3 x \right )^{{1}/{3}} c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 35

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]
 

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

✗ 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