Internal problem ID [1976]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y-x \left (x^{2} y-1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 45
dsolve(y(x)=x*(x^2*y(x)-1)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x +\sqrt {x^{2}-c_{1}}}{c_{1} x} \\ y \left (x \right ) &= \frac {x -\sqrt {x^{2}-c_{1}}}{c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.509 (sec). Leaf size: 77
DSolve[y[x]==x*(x^2*y[x]-1)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^2+\sqrt {-\frac {1}{x^3}} x^2 \sqrt {-x \left (x^2+c_1\right )}} \\ y(x)\to \frac {x}{x^3+\frac {\sqrt {-x \left (x^2+c_1\right )}}{\sqrt {-\frac {1}{x^3}}}} \\ y(x)\to 0 \\ \end{align*}