60.3.287 problem 1304

Internal problem ID [11283]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1304
Date solved : Sunday, March 30, 2025 at 08:07:55 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 38

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

\[ y = \frac {\operatorname {Ei}_{1}\left (\frac {1}{x}\right ) {\mathrm e}^{\frac {1}{x}} c_2 +c_1 \,{\mathrm e}^{\frac {1}{x}}-2 c_2 x \left (x^{2}-\frac {1}{2} x +\frac {1}{2}\right )}{x} \]

✓ Mathematica. Time used: 0.292 (sec). Leaf size: 44

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

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

✗ Sympy

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

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