50.5.2 problem 1(b)

Internal problem ID [7872]
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(b)
Date solved : Monday, January 27, 2025 at 03:29:15 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)-3*x*y(x)-2*y(x)^2=0,y(x), singsol=all)
 

\[ y = \frac {x^{3}}{-x^{2}+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 25

DSolve[x^2*D[y[x],x]-3*x*y[x]-2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x^3}{x^2-c_1} \\ y(x)\to 0 \\ \end{align*}