Internal problem ID [11688]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {2 x^{2}+y^{2}}{2 y x -x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 57
dsolve(diff(y(x),x)=(2*x^2+y(x)^2)/(2*x*y(x)-x^2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {c_{1} x -\sqrt {9 c_{1}^{2} x^{2}+4 c_{1} x}}{2 c_{1}} \\ y \left (x \right ) &= \frac {c_{1} x +\sqrt {9 c_{1}^{2} x^{2}+4 c_{1} x}}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.748 (sec). Leaf size: 93
DSolve[y'[x]==(2*x^2+y[x]^2)/(2*x*y[x]-x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {x \left (9 x-4 e^{c_1}\right )}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {x \left (9 x-4 e^{c_1}\right )}\right ) \\ y(x)\to \frac {1}{2} \left (x-3 \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (3 \sqrt {x^2}+x\right ) \\ \end{align*}