Internal problem ID [3976]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 10
Problem number: Recognizable Exact Differential equations. Integrating factors. Exercise 10.9,
page 90.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\arctan \left (y x \right )+\frac {y x -2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.328 (sec). Leaf size: 24
dsolve((arctan(x*y(x))+(x*y(x)-2*x*y(x)^2)/(1+x^2*y(x)^2))+((x^2-2*x^2*y(x))/(1+x^2*y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\tan \left (\RootOf \left (\textit {\_Z} x -\ln \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )+c_{1}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.18 (sec). Leaf size: 26
DSolve[(ArcTan[x*y[x]]+(x*y[x]-2*x*y[x]^2)/(1+x^2*y[x]^2))+((x^2-2*x^2*y[x])/(1+x^2*y[x]^2))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (x^2 y(x)^2+1\right )-x \text {ArcTan}(x y(x))=c_1,y(x)\right ] \]