Internal problem ID [12157]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 79.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {x^{2} y^{\prime }}{\left (-y+x \right )^{2}}-\frac {y^{2}}{\left (-y+x \right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(x^2/(x-y(x))^2*diff(y(x),x)- y(x)^2/(x-y(x))^2=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{c_{1} x +1} \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 21
DSolve[x^2/(x-y[x])^2*y'[x]- y[x]^2/(x-y[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{1-c_1 x} y(x)\to 0 \end{align*}