Internal problem ID [2880]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 131.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.035 (sec). Leaf size: 24
dsolve(diff(y(x),x) = exp(x)*(a+b*exp(-y(x))),y(x), singsol=all)
\[ y \relax (x ) = -\ln \left (\frac {a}{{\mathrm e}^{a \,{\mathrm e}^{x}+c_{1} a}-b}\right ) \]
✓ Solution by Mathematica
Time used: 0.972 (sec). Leaf size: 24
DSolve[y'[x]==Exp[x](a+b Exp[-y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (\frac {-b+e^{a \left (e^x+c_1\right )}}{a}\right ) \\ \end{align*}