54.3.185 problem 1199

Internal problem ID [12480]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1199
Date solved : Wednesday, October 01, 2025 at 01:45:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 35

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

\[ y = \left (\operatorname {Ei}_{1}\left (x \right ) {\mathrm e}^{x} c_2 \,x^{3}+{\mathrm e}^{x} c_1 \,x^{3}-c_2 \left (x^{2}-x +2\right )\right ) x \]

✓ Mathematica. Time used: 33.396 (sec). Leaf size: 54

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

\begin{align*} y(x)&\to e^{x+4} x^4 \left (\int _1^x\frac {e^{-K[1]-4} c_1}{K[1]^4}dK[1]+c_2\right )\\ y(x)&\to c_2 e^{x+4} x^4 \end{align*}

✓ Sympy. Time used: 0.736 (sec). Leaf size: 474

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

\[ \text {Solution too large to show} \]