44.6.42 problem 42

Internal problem ID [7186]
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 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 42
Date solved : Sunday, March 30, 2025 at 11:50:34 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Maple. Time used: 0.080 (sec). Leaf size: 27

ode:=diff(y(x),x)+piecewise(0 <= x and x <= 2,1,2 < x,5)*y(x) = 0; 
ic:=y(0) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 4 \left (\left \{\begin {array}{cc} 1 & x <0 \\ {\mathrm e}^{-x} & x <2 \\ {\mathrm e}^{-5 x +8} & 2\le x \end {array}\right .\right ) \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 32

ode=D[y[x],x]+Piecewise[{ {1,0<=x<=2},{5,x>2}}]*y[x]==0; 
ic={y[0]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 4 & x\leq 0 \\ 4 e^{8-5 x} & x>2 \\ 4 e^{-x} & \text {True} \\ \end {array} \\ \end {array} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Piecewise((1, (x >= 0) & (x <= 2)), (5, x > 2))*y(x) + Derivative(y(x), x),0) 
ics = {y(0): 4} 
dsolve(ode,func=y(x),ics=ics)