60.3.167 problem 1181

Internal problem ID [11163]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1181
Date solved : Sunday, March 30, 2025 at 07:44:37 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

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

\[ y = \frac {\left (c_1 \,\operatorname {Ei}_{1}\left (-\frac {1}{x}\right )+c_2 \right ) {\mathrm e}^{-\frac {1}{x}}}{x} \]

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 30

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

\[ y(x)\to \frac {e^{1-\frac {1}{x}} \left (c_1-e c_2 \operatorname {ExpIntegralEi}\left (\frac {1}{x}\right )\right )}{x} \]

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 2)) - y(x))/(3*x - 1) cannot be solved by the factorable group method