Internal problem ID [5451]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x^{2} y^{\prime }-3 x y-2 y^{2}=0} \end {gather*}
✓ 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)
\[ y \relax (x ) = \frac {x^{3}}{-x^{2}+c_{1}} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 24
DSolve[x^2*y'[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*}