Internal problem ID [3979]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise
10.12, page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {y^{2}-3 x y-2 x^{2}+\left (x y-x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 59
dsolve((y(x)^2-3*x*y(x)-2*x^2)+(x*y(x)-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1} x^{2}-\sqrt {2 c_{1}^{2} x^{4}+1}}{c_{1} x} \\ y \relax (x ) = \frac {c_{1} x^{2}+\sqrt {2 c_{1}^{2} x^{4}+1}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.324 (sec). Leaf size: 99
DSolve[(y[x]^2-3*x*y[x]-2*x^2)+(x*y[x]-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\frac {\sqrt {2 x^4+e^{2 c_1}}}{x} \\ y(x)\to x+\frac {\sqrt {2 x^4+e^{2 c_1}}}{x} \\ y(x)\to x-\frac {\sqrt {2} \sqrt {x^4}}{x} \\ y(x)\to \frac {\sqrt {2} \sqrt {x^4}}{x}+x \\ \end{align*}