78.1.7 problem 1 (h)

Internal problem ID [18062]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (h)
Date solved : Tuesday, January 28, 2025 at 08:28:32 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 27

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

\[ \arctan \left (\frac {x y}{\sqrt {1-x^{2} y^{2}}}\right )-y+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.369 (sec). Leaf size: 93

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

\[ \text {Solve}\left [\frac {\sqrt {-\left (x^2 y(x)^2-1\right )^2}}{x (x y(x)-1)}-\frac {y(x) \sqrt {1-x^2 y(x)^2} \text {arcsinh}\left (x \sqrt {-y(x)^2}\right )}{\sqrt {-y(x)^2} \sqrt {x^2 y(x)^2-1}}=c_1,y(x)\right ] \]