Internal problem ID [11682]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Riccati]
\[ \boxed {y x +y^{2}+2 x^{2} y^{\prime }=-2 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 49
dsolve((2*x^2+x*y(x)+y(x)^2)+(2*x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\left (c_{1} x -\sqrt {c_{1} x}-2\right ) x}{c_{1} x -1} \\ y \left (x \right ) &= -\frac {\left (c_{1} x +\sqrt {c_{1} x}-2\right ) x}{c_{1} x -1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.203 (sec). Leaf size: 47
DSolve[(2*x^2+x*y[x]+y[x]^2)+(2*x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x \left (\sqrt {x}-2 e^{c_1}\right )}{-\sqrt {x}+e^{c_1}} \\ y(x)\to -2 x \\ y(x)\to -x \\ \end{align*}