Internal problem ID [11647]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y+\left (y^{2} x +x -y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
dsolve(y(x)+(x*y(x)^2+x-y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\operatorname {RootOf}\left (c_{1}^{2} {\mathrm e}^{2 \textit {\_Z}}+2 x^{2} \textit {\_Z} +2 c_{1} {\mathrm e}^{\textit {\_Z}}+1\right )} c_{1} +1}{x} \]
✓ Solution by Mathematica
Time used: 0.206 (sec). Leaf size: 27
DSolve[y[x]+(x*y[x]^2+x-y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {1}{y(x)}+\frac {c_1 e^{-\frac {1}{2} y(x)^2}}{y(x)},y(x)\right ] \]