77.37.7 problem 7

Internal problem ID [20736]
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 : 7
Date solved : Thursday, October 02, 2025 at 06:22:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 20

ode:=x^2*diff(diff(y(x),x),x)+(-4*x^2+x)*diff(y(x),x)+(4*x^2-2*x+1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{2 x} \left (c_2 \,x^{-i}+c_1 \,x^{i}\right ) \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 35

ode=x^2*D[y[x],{x,2}]+(x-4*x^2)*D[y[x],x]+(1-2*x+4*x^2)*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{2 x} x^{-i} \left (2 c_1-i c_2 x^{2 i}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (-4*x**2 + x)*Derivative(y(x), x) + (4*x**2 - 2*x + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None