Internal problem ID [12153]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 75.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
\[ \boxed {\frac {y^{2}}{\left (-y+x \right )^{2}}+\left (\frac {1}{y}-\frac {x^{2}}{\left (-y+x \right )^{2}}\right ) y^{\prime }=\frac {1}{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve((y(x)^2/(x-y(x))^2-1/x )+(1/y(x)-x^2/(x-y(x))^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-\ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+x \ln \left (x \right )+{\mathrm e}^{\textit {\_Z}} c_{1} +\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} x -c_{1} x -x \textit {\_Z} \right )} \]
✓ Solution by Mathematica
Time used: 0.721 (sec). Leaf size: 29
DSolve[(y[x]^2/(x-y[x])^2-1/x )+(1/y[x]-x^2/(x-y[x])^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {y(x)^2}{x-y(x)}+y(x)-\log (y(x))+\log (x)=c_1,y(x)\right ] \]