60.3.237 problem 1253

Internal problem ID [11233]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1253
Date solved : Wednesday, March 05, 2025 at 01:57:19 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x \left (x +1\right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*(1+x)*diff(diff(y(x),x),x)+(3*x+2)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_{1} \ln \left (x +1\right )+c_{2}}{x} \]

✓ Mathematica. Time used: 0.301 (sec). Leaf size: 58

ode=y[x] + (2 + 3*x)*D[y[x],x] + x*(1 + x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\sqrt {x+1} (c_2 \log (2 (x+1))+2 c_1) \exp \left (-\frac {1}{2} \int _1^x\left (\frac {1}{K[1]+1}+\frac {2}{K[1]}\right )dK[1]\right )}{\sqrt {2}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(x + 1)*Derivative(y(x), (x, 2)) + (3*x + 2)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False