83.37.4 problem 4

Internal problem ID [19370]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (B) at page 128
Problem number : 4
Date solved : Thursday, March 13, 2025 at 02:20:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 39

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

\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x \left (b x +2 \sqrt {-b}\right )}{2}}+c_{2} {\mathrm e}^{\frac {x \left (b x -2 \sqrt {-b}\right )}{2}} \]

✓ Mathematica. Time used: 0.062 (sec). Leaf size: 63

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

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

✗ Sympy

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

False