64.5.28 problem 28

Internal problem ID [13270]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 28
Date solved : Monday, March 31, 2025 at 07:44:41 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6 \end{align*}

✓ Maple. Time used: 0.082 (sec). Leaf size: 40

ode:=diff(y(x),x)+y(x) = piecewise(0 <= x and x < 10,5,10 <= x,1); 
ic:=y(0) = 6; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \left \{\begin {array}{cc} 6 \,{\mathrm e}^{-x} & x <0 \\ {\mathrm e}^{-x}+5 & x <10 \\ {\mathrm e}^{-x}+4 \,{\mathrm e}^{10-x}+1 & 10\le x \end {array}\right . \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 45

ode=D[y[x],x]+y[x]==Piecewise[{{5,0<=x<10},{1,x>=10}}]; 
ic={y[0]==6}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 6 e^{-x} & x\leq 0 \\ e^{-x} \left (1+4 e^{10}+e^x\right ) & x>10 \\ 5+e^{-x} & \text {True} \\ \end {array} \\ \end {array} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-Piecewise((5, (x >= 0) & (x < 10)), (1, x >= 10)) + y(x) + Derivative(y(x), x),0) 
ics = {y(0): 6} 
dsolve(ode,func=y(x),ics=ics)