29.5.15 problem 131

Internal problem ID [4732]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 131
Date solved : Monday, January 27, 2025 at 09:34:45 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.161 (sec). Leaf size: 22

dsolve(diff(y(x),x) = exp(x)*(a+b*exp(-y(x))),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.142 (sec). Leaf size: 24

DSolve[D[y[x],x]==Exp[x](a+b Exp[-y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \log \left (\frac {-b+e^{a \left (e^x+c_1\right )}}{a}\right ) \]