Internal problem ID [7711]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 131.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.096 (sec). Leaf size: 34
dsolve((2*x+1)*diff(y(x),x) - 4*exp(-y(x)) + 2=0,y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (\frac {2 x +1}{-1+4 x \,{\mathrm e}^{2 c_{1}}+2 \,{\mathrm e}^{2 c_{1}}}\right )-2 c_{1} \]
✓ Solution by Mathematica
Time used: 0.439 (sec). Leaf size: 26
DSolve[(2*x+1)*y'[x] - 4*Exp[-y[x]] + 2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (2+\frac {e^{c_1}}{2 x+1}\right ) \\ y(x)\to \log (2) \\ \end{align*}