78.4.12 problem 13

Internal problem ID [18135]
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 : 13
Date solved : Tuesday, January 28, 2025 at 11:31:35 AM
CAS classification : [_exact, _rational, _Riccati]

\begin{align*} \frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve((y(x)+x*diff(y(x),x))/(1-x^2*y(x)^2)+x=0,y(x), singsol=all)
 

\[ y = \frac {i \tan \left (\frac {i x^{2}}{2}+c_1 \right )}{x} \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 25

DSolve[(y[x]+x*D[y[x],x])/(1-x^2*y[x]^2)+x==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\tanh \left (\frac {1}{2} \left (x^2-2 i c_1\right )\right )}{x} \]