51.1.67 problem 67

Internal problem ID [10337]
Book : First order enumerated odes
Section : section 1
Problem number : 67
Date solved : Tuesday, September 30, 2025 at 07:22:15 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=10+{\mathrm e}^{x +y} \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 21

ode:=diff(y(x),x) = 10+exp(x+y(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x +\ln \left (11\right )+\ln \left (\frac {1}{{\mathrm e}^{-11 x} c_1 -1}\right ) \]

✓ Mathematica. Time used: 2.655 (sec). Leaf size: 42

ode=D[y[x],x]==10+Exp[x+y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log \left (-\frac {11 e^{10 x+11 c_1}}{-1+e^{11 (x+c_1)}}\right )\\ y(x)&\to \log \left (-11 e^{-x}\right ) \end{align*}

✓ Sympy. Time used: 0.352 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = \log {\left (\frac {11 e^{10 x}}{C_{1} - e^{11 x}} \right )} \]