78.4.10 problem 11

Internal problem ID [18133]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 8 (Exact Equations). Problems at page 72
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 11:31:30 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: 0.006 (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)
 

\[ y = \frac {c_1 +{\mathrm e}^{2 x}}{x \left ({\mathrm e}^{2 x}-c_1 \right )} \]

✓ Solution by Mathematica

Time used: 0.156 (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]
 

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