60.3.188 problem 1202

Internal problem ID [11184]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1202
Date solved : Sunday, March 30, 2025 at 07:45:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 24

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

\[ y(x)\to \frac {1}{2} e x \left (c_2 e^{2 x}+2 c_1\right ) \]

✗ Sympy

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

False