Internal problem ID [3992]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.6, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x y}{x^{2}+1}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)-(2*x*y(x))/(x^2+1)=1,y(x), singsol=all)
\[ y \relax (x ) = \left (\arctan \relax (x )+c_{1}\right ) \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 16
DSolve[y'[x]-2*x*y[x]/(x^2+1)==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x^2+1\right ) (\text {ArcTan}(x)+c_1) \\ \end{align*}