Internal problem ID [1889]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{2}+y y^{\prime }+y^{\prime } y x^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(y(x)^2+y(x)*diff(y(x),x)+x^2*y(x)*diff(y(x),x)-1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {{\mathrm e}^{-2 \arctan \relax (x )} c_{1}+1} \\ y \relax (x ) = -\sqrt {{\mathrm e}^{-2 \arctan \relax (x )} c_{1}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.926 (sec). Leaf size: 55
DSolve[y[x]^2+y[x]*y'[x]+x^2*y[x]*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {1+e^{-2 \text {ArcTan}(x)+2 c_1}} \\ y(x)\to \sqrt {1+e^{-2 \text {ArcTan}(x)+2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}