82.54.6 problem Ex. 6

Internal problem ID [18951]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at end of chapter at page 120
Problem number : Ex. 6
Date solved : Monday, March 31, 2025 at 06:26:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 b y^{\prime }+b^{2} x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 47

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

\[ y = {\mathrm e}^{-\frac {b x \left (i x -2\right )}{2}} x \left (\operatorname {KummerU}\left (\frac {3}{4}-\frac {i b}{4}, \frac {3}{2}, i b \,x^{2}\right ) c_2 +\operatorname {KummerM}\left (\frac {3}{4}-\frac {i b}{4}, \frac {3}{2}, i b \,x^{2}\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.04 (sec). Leaf size: 75

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

\[ y(x)\to e^{\frac {1}{2} b (2-i x) x} \left (c_1 \operatorname {HermiteH}\left (\frac {1}{2} i (b+i),\sqrt [4]{-1} \sqrt {b} x\right )+c_2 \operatorname {Hypergeometric1F1}\left (-\frac {1}{4} i (b+i),\frac {1}{2},i b x^2\right )\right ) \]

✗ Sympy

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

False