Internal problem ID [4484]
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]
\[ \boxed {\arctan \left (x y\right )+\frac {x y-2 x y^{2}}{y^{2} x^{2}+1}+\frac {\left (x^{2}-2 y x^{2}\right ) y^{\prime }}{y^{2} x^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 22
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)
\[ y \left (x \right ) = \frac {\tan \left (\operatorname {RootOf}\left (x \textit {\_Z} -\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+c_{1} \right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.173 (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]
\[ \text {Solve}\left [\log \left (x^2 y(x)^2+1\right )-x \arctan (x y(x))=c_1,y(x)\right ] \]