Internal problem ID [1040]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {1}{x}+2 x +\left (\frac {1}{y}+2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve((1/x+2*x)+(1/y(x)+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-\frac {\LambertW \left (\frac {2 \,{\mathrm e}^{-2 x^{2}-2 c_{1}}}{x^{2}}\right )}{2}-x^{2}-c_{1}}}{x} \]
✓ Solution by Mathematica
Time used: 60.103 (sec). Leaf size: 66
DSolve[(1/x+2*x)+(1/y[x]+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\text {ProductLog}\left (\frac {2 e^{-2 x^2+2 c_1}}{x^2}\right )}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\text {ProductLog}\left (\frac {2 e^{-2 x^2+2 c_1}}{x^2}\right )}}{\sqrt {2}} \\ \end{align*}