68.15.7 problem 7

Internal problem ID [17733]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 7
Date solved : Thursday, October 02, 2025 at 02:27:29 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=2*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+20*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left (c_1 \sin \left (3 \ln \left (x \right )\right )+c_2 \cos \left (3 \ln \left (x \right )\right )\right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 24

ode=2*x^2*D[y[x],{x,2}]-2*x*D[y[x],x]+20*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) + 20*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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