54.3.251 problem 1267

Internal problem ID [12546]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1267
Date solved : Wednesday, October 01, 2025 at 02:06:30 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.021 (sec). Leaf size: 43

ode:=2*x^2*diff(diff(y(x),x),x)-(2*x^2+l-5*x)*diff(y(x),x)-(4*x-1)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{x -\frac {l}{2 x}} \left (c_1 \int \frac {{\mathrm e}^{\frac {-2 x^{2}+l}{2 x}}}{x^{{3}/{2}}}d x +2 c_2 \right )}{2 \sqrt {x}} \]

✓ Mathematica. Time used: 0.345 (sec). Leaf size: 59

ode=(1 - 4*x)*y[x] - (l - 5*x + 2*x^2)*D[y[x],x] + 2*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{x-\frac {l}{2 x}} \left (c_2 \int _1^x\frac {e^{\frac {l}{2 K[1]}-K[1]}}{K[1]^{3/2}}dK[1]+c_1\right )}{\sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
l = symbols("l") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - (4*x - 1)*y(x) - (l + 2*x**2 - 5*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (2*x**2*Derivative(y(x), (x, 2)) - 4*x*y(x) + y(x))/(l + 2*x**2 - 5*x) cannot be solved by the factorable group method