54.3.189 problem 1203

Internal problem ID [12484]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1203
Date solved : Wednesday, October 01, 2025 at 01:45:40 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 83

ode=-2*y[x] + a*x^2*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 {2 a x^{3/2} e^{\frac {1}{2}-\frac {a x}{2}} \left ((a c_1 x+2 i c_2) \cosh \left (\frac {a x}{2}\right )-(i a c_2 x+2 c_1) \sinh \left (\frac {a x}{2}\right )\right )}{\sqrt {\pi } (-i a x)^{5/2}} \end{align*}

✗ Sympy

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

False