Internal problem ID [12967]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y = \left \{\begin {array}{cc} 0 & x <1 \\ -1+x & x <2 \\ 1 & 2\le x \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 23
DSolve[{y'[x]==Piecewise[{{0,x<1},{1,1<=x<2},{0,2<=x}}],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & x\leq 1 \\ x-1 & 1<x\leq 2 \\ 1 & \text {True} \\ \end {array} \\ \end {array} \]