Internal problem ID [2695]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 60.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
Solve \begin {gather*} \boxed {y^{2}+\left (y x +y^{2}-1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(y(x)^2+(x*y(x)+y(x)^2-1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (-{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x +2 c_{1}+2 \textit {\_Z} \right )} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 30
DSolve[y[x]^2+(x*y[x]+y[x]^2-1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {\log (y(x))-\frac {y(x)^2}{2}}{y(x)}+\frac {c_1}{y(x)},y(x)\right ] \]