Internal problem ID [2517]
Book: Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section: Exercises, page 14
Problem number: 2(o).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x +\left (2-x +2 y\right ) y^{\prime }-x y \left (y^{\prime }-1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 17
dsolve(x+(2-x+2*y(x))*diff(y(x),x)=x*y(x)*(diff(y(x),x)-1),y(x), singsol=all)
\begin{align*} y \relax (x ) = -1 \\ y \relax (x ) = x +2 \ln \left (-2+x \right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[x+(2-x+2*y[x])*y'[x]==x*y[x]*(y'[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1 \\ y(x)\to x+2 \log (x-2)+c_1 \\ \end{align*}