50.1.5 problem 5

Internal problem ID [10003]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 06:46:15 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y+1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(x),x) = 1+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -1+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 18

ode=D[y[x],x] == y[x]+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -1+c_1 e^x\\ y(x)&\to -1 \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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