Internal problem ID [982]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }+2 y x -\frac {1}{\left (x^{2}+1\right ) y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 38
dsolve((1+x^2)*diff(y(x),x)+2*x*y(x)=1/((1+x^2)*y(x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {2 x +c_{1}}}{x^{2}+1} \\ y \relax (x ) = -\frac {\sqrt {2 x +c_{1}}}{x^{2}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.295 (sec). Leaf size: 46
DSolve[(1+x^2)*y'[x]+2*x*y[x]==1/((1+x^2)*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {2 x+c_1}}{x^2+1} \\ y(x)\to \frac {\sqrt {2 x+c_1}}{x^2+1} \\ \end{align*}