54.3.173 problem 1187

Internal problem ID [12468]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1187
Date solved : Wednesday, October 01, 2025 at 01:45:28 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 52

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

\[ y = x^{-\frac {a}{2}} \sqrt {x}\, \left (x^{\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_1 +x^{-\frac {\sqrt {a^{2}-2 a -4 b +1}}{2}} c_2 \right ) \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 57

ode=b*y[x] + a*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 x^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 b+1}-a+1\right )} \left (c_2 x^{\sqrt {a^2-2 a-4 b+1}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 1.228 (sec). Leaf size: 617

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

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