50.5.7 problem 1(g)

Internal problem ID [7877]
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 : Monday, January 27, 2025 at 03:30:15 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

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

\[ y = \frac {2 x}{7}+\frac {c_{1}}{x^{6}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 17

DSolve[x*D[y[x],x]==2*x-6*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x}{7}+\frac {c_1}{x^6} \]