29.9.3 problem 243

Internal problem ID [4843]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 243
Date solved : Monday, January 27, 2025 at 09:42:25 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 31

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

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

✓ Solution by Mathematica

Time used: 0.715 (sec). Leaf size: 26

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