60.3.109 problem 1123

Internal problem ID [11105]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1123
Date solved : Sunday, March 30, 2025 at 07:42:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

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

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

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 53

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

\[ y(x)\to e^{-\frac {1}{2} x^2 \left (\sqrt {a^2-b}-a\right )} \left (c_2 e^{x^2 \sqrt {a^2-b}}+c_1\right ) \]

✗ Sympy

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

False