Internal problem ID [2620]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, End of chapter, page 61
Problem number: 20.
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 (x^{2}-y x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 59
dsolve((y(x)^2-3*x*y(x)-2*x^2)=(x^2-x*y(x))*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{2} c_{1}-\sqrt {2 x^{4} c_{1}^{2}+1}}{c_{1} x} \\ y \relax (x ) = \frac {x^{2} c_{1}+\sqrt {2 x^{4} c_{1}^{2}+1}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.724 (sec). Leaf size: 99
DSolve[(y[x]^2-3*x*y[x]-2*x^2)==(x^2-x*y[x])*y'[x],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*}