26.2.11 problem 11

Internal problem ID [4260]
Book : Differential equations with applications and historial notes, George F. Simmons. Second edition. 1971
Section : Chapter 2, section 8, page 41
Problem number : 11
Date solved : Monday, January 27, 2025 at 08:46:43 AM
CAS classification : [_exact, _rational, _Riccati]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

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)
 

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

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 18

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

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