Internal problem ID [12438]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-y^{2} x +\left (y-x^{2} y\right ) y^{\prime }=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve((x-y(x)^2*x)+(y(x)-x^2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\left (x^{2}-1\right ) \left (x^{2}+c_{1} \right )}}{x^{2}-1} \\ y \left (x \right ) &= -\frac {\sqrt {\left (x^{2}-1\right ) \left (x^{2}+c_{1} \right )}}{x^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.652 (sec). Leaf size: 74
DSolve[(x-y[x]^2*x)+(y[x]-x^2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2-1-e^{2 c_1}}}{\sqrt {x^2-1}} \\ y(x)\to \frac {\sqrt {x^2-1-e^{2 c_1}}}{\sqrt {x^2-1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}