60.3.335 problem 1352

Internal problem ID [11331]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1352
Date solved : Sunday, March 30, 2025 at 08:17:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 42

ode:=diff(diff(y(x),x),x) = -2/x^2*(x+a)*diff(y(x),x)-b/x^4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {2 \sqrt {a^{2}-b}}{x}}+c_1 \right ) {\mathrm e}^{\frac {a -\sqrt {a^{2}-b}}{x}} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 51

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-b*y(x) - x**4*Derivative(y(x), (x, 2)))/(2*x**2*(a + x)) cannot be solved by the factorable group method