Internal problem ID [4022]
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]]
\[ \boxed {y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve(y(x)+(1+y(x)^2*exp(2*x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{-x}}{\sqrt {\operatorname {LambertW}\left (c_{1} {\mathrm e}^{-2 x}\right )}} \]
✓ Solution by Mathematica
Time used: 3.361 (sec). Leaf size: 57
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 {W\left (e^{-2 x+2 c_1}\right )}} \\ y(x)\to \frac {e^{-x}}{\sqrt {W\left (e^{-2 x+2 c_1}\right )}} \\ y(x)\to 0 \\ \end{align*}