Internal problem ID [4042]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.29, page 103.
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 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 59
dsolve((x*y(x)-x^2)*diff(y(x),x)+y(x)^2-3*x*y(x)-2*x^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1} x^{2}-\sqrt {2 x^{4} c_{1}^{2}+1}}{c_{1} x} \\ y \relax (x ) = \frac {c_{1} x^{2}+\sqrt {2 x^{4} c_{1}^{2}+1}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.024 (sec). Leaf size: 99
DSolve[(x*y[x]-x^2)*y'[x]+y[x]^2-3*x*y[x]-2*x^2==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*}