6.10 problem Exercise 12.10, page 103

Internal problem ID [4023]

Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number: Exercise 12.10, page 103.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.052 (sec). Leaf size: 18

dsolve(y(x)+(1+y(x)^2*exp(2*x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \relax (x ) = \frac {{\mathrm e}^{-x}}{\sqrt {\LambertW \left (c_{1} {\mathrm e}^{-2 x}\right )}} \]

Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 52

DSolve[y[x]+(1+y[x]^2*Exp[2*x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {e^{-x}}{\sqrt {\text {ProductLog}\left (e^{-2 x+2 c_1}\right )}} \\ y(x)\to \frac {e^{-x}}{\sqrt {\text {ProductLog}\left (e^{-2 x+2 c_1}\right )}} \\ \end{align*}