47.1.24 problem 24

Internal problem ID [7405]
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
Date solved : Monday, January 27, 2025 at 02:53:07 PM
CAS classification : [_separable]

\begin{align*} z^{\prime }&=10^{x +z} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(z(x),x)=10^(x+z(x)),z(x), singsol=all)
 

\[ z = \frac {\ln \left (-\frac {1}{c_{1} \ln \left (2\right )+c_{1} \ln \left (5\right )+10^{x}}\right )}{\ln \left (2\right )+\ln \left (5\right )} \]

✓ Solution by Mathematica

Time used: 0.944 (sec). Leaf size: 24

DSolve[D[z[x],x]==10^(x+z[x]),z[x],x,IncludeSingularSolutions -> True]
 

\[ z(x)\to -\frac {\log \left (-10^x+c_1 (-\log (10))\right )}{\log (10)} \]