51.1.10 problem 10

Internal problem ID [10280]
Book : First order enumerated odes
Section : section 1
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 07:16:31 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

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

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

✓ Sympy. Time used: 0.058 (sec). Leaf size: 8

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

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