Internal problem ID [4984]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {z^{\prime }-10^{x +z}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(diff(z(x),x)=10^(x+z(x)),z(x), singsol=all)
\[ z \relax (x ) = \frac {\ln \left (-\frac {1}{c_{1} \ln \left (10\right )+10^{x}}\right )}{\ln \left (10\right )} \]
✓ Solution by Mathematica
Time used: 1.468 (sec). Leaf size: 24
DSolve[z'[x]==10^(x+z[x]),z[x],x,IncludeSingularSolutions -> True]
\begin{align*} z(x)\to -\frac {\log \left (-10^x+c_1 (-\log (10))\right )}{\log (10)} \\ \end{align*}