Internal problem ID [5439]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.5. Exact Equations. Page
20
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, _Riccati]
Solve \begin {gather*} \boxed {\frac {y}{1-y^{2} x^{2}}+\frac {x y^{\prime }}{1-y^{2} x^{2}}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(y(x)/(1-x^2*y(x)^2)+x/(1-x^2*y(x)^2)*diff(y(x),x)=1,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: 0.248 (sec). Leaf size: 18
DSolve[y[x]/(1-x^2*y[x]^2)+x/(1-x^2*y[x]^2)*y'[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\tanh (x+i c_1)}{x} \\ \end{align*}