60.3.199 problem 1213

Internal problem ID [11195]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1213
Date solved : Sunday, March 30, 2025 at 07:45:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 53

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

\[ y = \left (\operatorname {BesselI}\left (-\frac {1}{6}, \frac {x^{3}}{6}\right ) c_1 +\operatorname {BesselI}\left (\frac {5}{6}, \frac {x^{3}}{6}\right ) c_1 -c_2 \left (-\operatorname {BesselK}\left (\frac {5}{6}, \frac {x^{3}}{6}\right )+\operatorname {BesselK}\left (\frac {1}{6}, \frac {x^{3}}{6}\right )\right )\right ) x^{{3}/{2}} {\mathrm e}^{-\frac {x^{3}}{6}} \]

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 54

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

\[ y(x)\to \frac {\sqrt [3]{3} c_1 \operatorname {Hypergeometric1F1}\left (-\frac {1}{3},\frac {1}{3},-\frac {x^3}{3}\right )}{x}+\frac {c_2 x \operatorname {Hypergeometric1F1}\left (\frac {1}{3},\frac {5}{3},-\frac {x^3}{3}\right )}{\sqrt [3]{3}} \]

✗ Sympy

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

False