83.49.8 problem Ex 8 page 126

Internal problem ID [19550]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 8 page 126
Date solved : Monday, March 31, 2025 at 07:33:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 17

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

\[ y(x)\to e^x x (c_2 x+c_1) \]

✗ Sympy

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

False