Internal problem ID [6192]
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]
\[ \boxed {\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}=1} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} c_{1} +1}{x \left ({\mathrm e}^{-2 x} c_{1} -1\right )} \]
✓ Solution by Mathematica
Time used: 0.16 (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]
\[ y(x)\to \frac {\tanh (x+i c_1)}{x} \]