56.1.8 problem 8

Internal problem ID [8720]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 8
Date solved : Sunday, March 30, 2025 at 01:24:50 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 8

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

\[ y = c_1 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 16

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

\begin{align*} y(x)\to c_1 e^x \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.036 (sec). Leaf size: 7

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

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