7.7.1 problem 1

Internal problem ID [179]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 1
Date solved : Saturday, March 29, 2025 at 04:38:30 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

\[ y = \left (\ln \left (x \right )+c_1 \right ) x^{3} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 14

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

\[ y(x)\to x^3 (\log (x)+c_1) \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 10

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

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