59.1.357 problem 364

Internal problem ID [9529]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 364
Date solved : Wednesday, March 05, 2025 at 07:50:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+2*x^2*diff(y(x),x)+(x^4+2*x-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 34

ode=D[y[x],{x,2}]+2*x^2*D[y[x],x]+(x^4+2*x-1)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), x) + (x**4 + 2*x - 1)*y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False