54.3.140 problem 1154

Internal problem ID [12435]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1154
Date solved : Friday, October 03, 2025 at 03:19:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.052 (sec). Leaf size: 53

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

\[ y = c_1 \operatorname {WhittakerM}\left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right )+c_2 \operatorname {WhittakerW}\left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 88

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

\begin{align*} y(x)&\to c_1 M_{-\frac {i b}{2 \sqrt {a}},-\frac {1}{2} i \sqrt {4 c-1}}\left (2 i \sqrt {a} x\right )+c_2 W_{-\frac {i b}{2 \sqrt {a}},-\frac {1}{2} i \sqrt {4 c-1}}\left (2 i \sqrt {a} x\right ) \end{align*}

✗ Sympy

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

ValueError : Expected Expr or iterable but got None