Internal problem ID [2044]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-y^{\prime } x +y-2 y^{2}-2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(y(x)-x*diff(y(x),x)=2*(y(x)^2+diff(y(x),x)),y(x), singsol=all)
\[ y = \frac {x +2}{2 x +c_{1}} \]
✓ Solution by Mathematica
Time used: 0.39 (sec). Leaf size: 32
DSolve[y[x]-x*y'[x]==2*(y[x]^2+y'[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+2}{2 x+4+e^{c_1}} y(x)\to 0 y(x)\to \frac {1}{2} \end{align*}