67.1.43 problem 2.9 a

Internal problem ID [16308]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.9 a
Date solved : Thursday, October 02, 2025 at 10:45:35 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 13

ode:=diff(y(x),x) = piecewise(x < 0,0,0 <= x,1); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \left \{\begin {array}{cc} 0 & x <0 \\ x & 0\le x \end {array}\right . \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 9

ode=D[y[x],x]==UnitStep[x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \theta (x) \end{align*}

✓ Sympy. Time used: 0.116 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = x \]