Internal problem ID [15077]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 189.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]
\[ \boxed {-x^{2} y+x^{2} \left (y-x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 51
dsolve(( 1-x^2*y(x))+x^2*(y(x)-x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}+\sqrt {x \left (x^{3}-2 c_{1} x +2\right )}}{x} \\ y \left (x \right ) &= \frac {x^{2}-\sqrt {x \left (x^{3}-2 c_{1} x +2\right )}}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.493 (sec). Leaf size: 66
DSolve[( 1-x^2*y[x])+x^2*(y[x]-x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+\sqrt {-\frac {1}{x^2}} \sqrt {-x \left (x^3+c_1 x+2\right )} \\ y(x)\to x-\sqrt {-\frac {1}{x^2}} \sqrt {-x \left (x^3+c_1 x+2\right )} \\ \end{align*}