60.3.12 problem 1012

Internal problem ID [11008]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1012
Date solved : Thursday, March 13, 2025 at 08:23:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.250 (sec). Leaf size: 29

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

\[ y = \frac {c_{1} \operatorname {WhittakerM}\left (-\frac {a}{4}, \frac {1}{4}, x^{2}\right )+c_{2} \operatorname {WhittakerW}\left (-\frac {a}{4}, \frac {1}{4}, x^{2}\right )}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 47

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

\[ y(x)\to c_1 \operatorname {ParabolicCylinderD}\left (\frac {1}{2} (-a-1),\sqrt {2} x\right )+c_2 \operatorname {ParabolicCylinderD}\left (\frac {a-1}{2},i \sqrt {2} x\right ) \]

✗ Sympy

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

False