Internal problem ID [2590]
Book: Differential equations with applications and historial notes, George F. Simmons,
1971
Section: Chapter 2, section 8, page 41
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, _Riccati]
Solve \begin {gather*} \boxed {1-\frac {y}{1-x^{2} y^{2}}-\frac {x y^{\prime }}{1-x^{2} y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 27
dsolve(1=y(x)/(1-x^2*y(x)^2)+x/(1-x^2*y(x)^2)*diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-2 x} c_{1}+1}{x \left ({\mathrm e}^{-2 x} c_{1}-1\right )} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 18
DSolve[1==y[x]/(1-x^2*y[x]^2)+x/(1-x^2*y[x]^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\tanh (x+i c_1)}{x} \\ \end{align*}