51.1.18 problem 18

Internal problem ID [10288]
Book : First order enumerated odes
Section : section 1
Problem number : 18
Date solved : Tuesday, September 30, 2025 at 07:17:18 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.070 (sec). Leaf size: 10

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

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