74.18.54 problem 60

Internal problem ID [16540]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 60
Date solved : Monday, March 31, 2025 at 02:55:59 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

ode:=5*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{3}/{5}} \left (c_1 \sin \left (\frac {\ln \left (x \right )}{5}\right )+c_2 \cos \left (\frac {\ln \left (x \right )}{5}\right )\right ) \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 32

ode=5*x^2*D[y[x],{x,2}]-x*D[y[x],x]+2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^{3/5} \left (c_2 \cos \left (\frac {\log (x)}{5}\right )+c_1 \sin \left (\frac {\log (x)}{5}\right )\right ) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{\frac {3}{5}} \left (C_{1} \sin {\left (\frac {\log {\left (x \right )}}{5} \right )} + C_{2} \cos {\left (\frac {\log {\left (x \right )}}{5} \right )}\right ) \]