Internal problem ID [11632]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {2 y x +3 y^{2}-\left (2 y x +x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 35
dsolve((2*x*y(x)+3*y(x)^2)- (2*x*y(x)+x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \left (-\frac {1}{2}-\frac {\sqrt {4 x c_{1} +1}}{2}\right ) x y \left (x \right ) = \left (-\frac {1}{2}+\frac {\sqrt {4 x c_{1} +1}}{2}\right ) x \end{align*}
✓ Solution by Mathematica
Time used: 0.618 (sec). Leaf size: 61
DSolve[(2*x*y[x]+3*y[x]^2)- (2*x*y[x]+x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} x \left (1+\sqrt {1+4 e^{c_1} x}\right ) y(x)\to \frac {1}{2} x \left (-1+\sqrt {1+4 e^{c_1} x}\right ) y(x)\to 0 y(x)\to -x \end{align*}