54.3.187 problem 1201

Internal problem ID [12482]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1201
Date solved : Wednesday, October 01, 2025 at 01:45:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 31

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

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

✓ Mathematica. Time used: 0.171 (sec). Leaf size: 55

ode=-4*y[x] + x*(1 + 2*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 \frac {e^{-2 x} (2 x+3) \left (c_2 \int _1^x\frac {4 e^{2 K[1]} K[1]^3}{(2 K[1]+3)^2}dK[1]+c_1\right )}{2 x^2} \end{align*}

✓ Sympy. Time used: 0.459 (sec). Leaf size: 374

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

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