Internal problem ID [12116]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y-y^{\prime } x -y^{\prime } y x^{2}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 49
dsolve(y(x)-x*diff(y(x),x)=x^2*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {-c_{1} +\sqrt {c_{1}^{2}+x^{2}}}{c_{1} x} \\ y \left (x \right ) &= \frac {-c_{1} -\sqrt {c_{1}^{2}+x^{2}}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.786 (sec). Leaf size: 68
DSolve[y[x]-x*y'[x]==x^2*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1+\sqrt {\frac {1}{x^2}} x \sqrt {1+c_1 x^2}}{x} \\ y(x)\to -\frac {1}{x}+\sqrt {\frac {1}{x^2}} \sqrt {1+c_1 x^2} \\ y(x)\to 0 \\ \end{align*}