61.29.5 problem 114

Internal problem ID [12535]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.2-4
Problem number : 114
Date solved : Monday, March 31, 2025 at 05:38:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

\[ y = c_1 \,x^{b} {\mathrm e}^{a x}+c_2 \operatorname {WhittakerM}\left (-b , -b +\frac {1}{2}, 2 a x \right ) \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 38

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

\[ y(x)\to c_1 M_{-b,b-\frac {1}{2}}(2 a x)+c_2 W_{-b,b-\frac {1}{2}}(2 a x) \]

✗ Sympy

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

ValueError : Expected Expr or iterable but got None