41.1.24 problem 24

Internal problem ID [8691]
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 : Tuesday, September 30, 2025 at 05:41:32 PM
CAS classification : [_separable]

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

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

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

\[ z = \frac {\ln \left (-\frac {1}{c_1 \ln \left (5\right )+c_1 \ln \left (2\right )+10^{x}}\right )}{\ln \left (2\right )+\ln \left (5\right )} \]

✓ Mathematica. Time used: 0.69 (sec). Leaf size: 24

ode=D[z[x],x]==10^(x+z[x]); 
ic={}; 
DSolve[{ode,ic},z[x],x,IncludeSingularSolutions->True]
 

\begin{align*} z(x)&\to -\frac {\log \left (-10^x+c_1 (-\log (10))\right )}{\log (10)} \end{align*}

✓ Sympy. Time used: 0.164 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
z = Function("z") 
ode = Eq(-10**(x + z(x)) + Derivative(z(x), x),0) 
ics = {} 
dsolve(ode,func=z(x),ics=ics)
 

\[ z{\left (x \right )} = \frac {\log {\left (- \frac {1}{10^{x} + C_{1}} \right )}}{\log {\left (10 \right )}} \]