44.1.32 problem 34

Internal problem ID [6907]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 34
Date solved : Sunday, March 30, 2025 at 11:28:01 AM
CAS classification : [_quadrature]

\begin{align*} 5 y^{\prime }&=2 y \end{align*}

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

ode:=5*diff(y(x),x) = 2*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {2 x}{5}} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 20

ode=5*D[y[x],x]==2*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 e^{2 x/5} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) + 5*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{\frac {2 x}{5}} \]