35.7.10 problem 16 (a)

Internal problem ID [6192]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 16 (a)
Date solved : Wednesday, March 05, 2025 at 12:24:12 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

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

\[ y = \frac {c_{1} x^{4}+c_{2}}{x^{3}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

\[ y(x)\to \frac {c_1}{x^3}+c_2 x \]

✓ Sympy. Time used: 0.162 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{3}} + C_{2} x \]