50.4.11 problem 11

Internal problem ID [7860]
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
Date solved : Monday, January 27, 2025 at 03:27:53 PM
CAS classification : [_exact, _rational, _Riccati]

\begin{align*} \frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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)
 

\[ y = \frac {{\mathrm e}^{2 x}+c_{1}}{x \left ({\mathrm e}^{2 x}-c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 18

DSolve[y[x]/(1-x^2*y[x]^2)+x/(1-x^2*y[x]^2)*D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\tanh (x+i c_1)}{x} \]