54.3.53 problem 1058

Internal problem ID [12348]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1058
Date solved : Wednesday, October 01, 2025 at 01:43:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 29

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

\[ y = {\mathrm e}^{\frac {x^{3}}{3}} \left (c_2 \int {\mathrm e}^{\frac {1}{4} x^{4}-\frac {1}{3} x^{3}}d x +c_1 \right ) \]

✓ Mathematica. Time used: 0.273 (sec). Leaf size: 44

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

\begin{align*} y(x)&\to e^{\frac {x^3}{3}} \left (c_2 \int _1^xe^{\frac {1}{12} K[1]^3 (3 K[1]-4)}dK[1]+c_1\right ) \end{align*}

✗ Sympy

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

False