60.4.34 problem 1490

Internal problem ID [11457]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1490
Date solved : Wednesday, March 05, 2025 at 02:26:18 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.019 (sec). Leaf size: 18

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

\[ y = c_{1} +c_{2} x \operatorname {BesselJ}\left (1, x\right )+c_3 x \operatorname {BesselY}\left (1, x\right ) \]

✓ Mathematica. Time used: 60.026 (sec). Leaf size: 33

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

\[ y(x)\to \int _1^x(\operatorname {BesselJ}(0,K[1]) c_1+\operatorname {BesselY}(0,K[1]) c_2) K[1]dK[1]+c_3 \]

✗ Sympy

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

NotImplementedError : The given ODE -x*(-x*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 2)))/(x**2 + 1) + Derivative(y(x), x) cannot be solved by the factorable group method