44.5.7 problem 1(g)

Internal problem ID [9163]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page 28
Problem number : 1(g)
Date solved : Tuesday, September 30, 2025 at 06:10:56 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=2 x -6 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x*diff(y(x),x) = 2*x-6*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x}{7}+\frac {c_1}{x^{6}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 17

ode=x*D[y[x],x]==2*x-6*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x}{7}+\frac {c_1}{x^6} \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 2*x + 6*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{6}} + \frac {2 x}{7} \]