Internal problem ID [3129]
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`]]
\[ \boxed {y^{2}-3 y x -\left (x^{2}-y x \right ) y^{\prime }=2 x^{2}} \]
✓ Solution by Maple
Time used: 0.032 (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 \left (x \right ) = \frac {c_{1} x^{2}-\sqrt {2 c_{1}^{2} x^{4}+1}}{c_{1} x} y \left (x \right ) = \frac {c_{1} x^{2}+\sqrt {2 c_{1}^{2} x^{4}+1}}{c_{1} x} \end{align*}
✓ Solution by Mathematica
Time used: 0.701 (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*}