15.16.1 problem 1

Internal problem ID [3221]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 1
Date solved : Sunday, March 30, 2025 at 01:21:40 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

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

\[ y = x^{{5}/{2}} \left (x^{\frac {\sqrt {21}}{2}} c_1 +x^{-\frac {\sqrt {21}}{2}} c_2 \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 34

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

\[ y(x)\to x^{\frac {5}{2}-\frac {\sqrt {21}}{2}} \left (c_2 x^{\sqrt {21}}+c_1\right ) \]

✓ Sympy. Time used: 0.164 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} x^{\frac {5}{2} - \frac {\sqrt {21}}{2}} + C_{2} x^{\frac {\sqrt {21}}{2} + \frac {5}{2}} \]