73.1.45 problem 2.9 c

Internal problem ID [15023]
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 c
Date solved : Tuesday, January 28, 2025 at 07:27:42 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 19

dsolve([diff(y(x),x)=piecewise(x<1,0,1<=x and x<2,1,2<=x,0),y(0) = 0],y(x), singsol=all)
 

\[ y = \left \{\begin {array}{cc} 0 & x <1 \\ x -1 & x <2 \\ 1 & 2\le x \end {array}\right . \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 23

DSolve[{D[y[x],x]==Piecewise[{{0,x<1},{1,1<=x<2},{0,2<=x}}],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & x\leq 1 \\ x-1 & 1<x\leq 2 \\ 1 & \text {True} \\ \end {array} \\ \end {array} \]