Internal problem ID [3099]
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]
\[ \boxed {-\frac {y}{1-y^{2} x^{2}}-\frac {x y^{\prime }}{1-y^{2} x^{2}}=-1} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} c_{1} +1}{x \left ({\mathrm e}^{-2 x} c_{1} -1\right )} \]
✓ Solution by Mathematica
Time used: 0.153 (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]
\[ y(x)\to \frac {\tanh (x+i c_1)}{x} \]