Internal problem ID [2991]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 243.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1+2 x \right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve((1+2*x)*diff(y(x),x) = 4*exp(-y(x))-2,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: 0.665 (sec). Leaf size: 26
DSolve[(1+2 x)y'[x]==4 Exp[-y[x]]-2,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*}