54.3.302 problem 1319

Internal problem ID [12597]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1319
Date solved : Wednesday, October 01, 2025 at 02:12:45 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (x^{2}+2\right ) y^{\prime \prime }-y^{\prime }-6 x y&=0 \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 31

ode:=x*(x^2+2)*diff(diff(y(x),x),x)-diff(y(x),x)-6*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x^{2}+2\right )^{{3}/{4}} \left (x^{{3}/{2}} c_1 +\operatorname {hypergeom}\left (\left [-\frac {3}{4}, \frac {7}{4}\right ], \left [\frac {1}{4}\right ], -\frac {x^{2}}{2}\right ) c_2 \right ) \]

✓ Mathematica. Time used: 0.136 (sec). Leaf size: 109

ode=-6*x*y[x] - D[y[x],x] + x*(2 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {6 K[1]^2+5}{2 K[1]^3+4 K[1]}dK[1]-\frac {1}{2} \int _1^x-\frac {1}{K[2]^3+2 K[2]}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {6 K[1]^2+5}{2 K[1]^3+4 K[1]}dK[1]\right )dK[3]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x**2 + 2)*Derivative(y(x), (x, 2)) - 6*x*y(x) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False