Internal problem ID [5727]
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]
\[ \boxed {-\left (1+{\mathrm e}^{x}\right ) y y^{\prime }=-{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 19
dsolve([exp(x)-(1+exp(x))*y(x)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {1-2 \ln \left (2\right )+2 \ln \left ({\mathrm e}^{x}+1\right )} \]
✓ Solution by Mathematica
Time used: 0.182 (sec). Leaf size: 23
DSolve[{Exp[x]-(1+Exp[x])*y[x]*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {2 \log \left (e^x+1\right )+1-\log (4)} \]