Internal problem ID [5441]
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: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, _Riccati]
Solve \begin {gather*} \boxed {\frac {x y^{\prime }+y}{1-y^{2} x^{2}}+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 19
dsolve((y(x)+x*diff(y(x),x))/(1-x^2*y(x)^2)+x=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {i \tan \left (\frac {i x^{2}}{2}+c_{1}\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 25
DSolve[(y[x]+x*y'[x])/(1-x^2*y[x]^2)+x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\tanh \left (\frac {1}{2} \left (x^2-2 i c_1\right )\right )}{x} \\ \end{align*}