60.3.264 problem 1280

Internal problem ID [11260]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1280
Date solved : Sunday, March 30, 2025 at 08:04:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }-\left (4 x^{2}+12 x +3\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.015 (sec). Leaf size: 36

ode:=4*x^2*diff(diff(y(x),x),x)+8*x*diff(y(x),x)-(4*x^2+12*x+3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{x} x^{2} \left (4 \,\operatorname {Ei}_{1}\left (2 x \right ) c_2 +c_1 \right )+{\mathrm e}^{-x} c_2 \left (-2 x +1\right )}{x^{{3}/{2}}} \]

✓ Mathematica. Time used: 0.298 (sec). Leaf size: 38

ode=(-3 - 12*x - 4*x^2)*y[x] + 8*x*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \sqrt {x} \left (c_2 \int _1^x\frac {e^{-2 K[1]}}{K[1]^3}dK[1]+c_1\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 8*x*Derivative(y(x), x) - (4*x**2 + 12*x + 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False