44.5.5 problem 5

Internal problem ID [7067]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 5
Date solved : Sunday, March 30, 2025 at 11:37:26 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=4 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

ode:=x*diff(y(x),x) = 4*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,x^{4} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 16

ode=x*D[y[x],x]==4*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x^4 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.144 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x^{4} \]