Internal problem ID [4974]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {{\mathrm e}^{x}-\left (1+{\mathrm e}^{x}\right ) y y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.123 (sec). Leaf size: 19
dsolve([exp(x)-(1+exp(x))*y(x)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {2 \ln \left ({\mathrm e}^{x}+1\right )-2 \ln \relax (2)+1} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 23
DSolve[{Exp[x]-(1+Exp[x])*y[x]*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {2 \log \left (e^x+1\right )+1-\log (4)} \\ \end{align*}