60.1.130 problem 131

Internal problem ID [10144]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 131
Date solved : Monday, January 27, 2025 at 06:29:52 PM
CAS classification : [_separable]

\begin{align*} \left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 31

dsolve((2*x+1)*diff(y(x),x) - 4*exp(-y(x)) + 2=0,y(x), singsol=all)
 

\[ y = -\ln \left (\frac {2 x +1}{-1+\left (4 x +2\right ) {\mathrm e}^{2 c_{1}}}\right )-2 c_{1} \]

✓ Solution by Mathematica

Time used: 0.682 (sec). Leaf size: 26

DSolve[(2*x+1)*D[y[x],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*}