Internal problem ID [13286]
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 b.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([diff(y(x),x)=piecewise(x<1,0,x>=1,1),y(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \left \{\begin {array}{cc} 2 & x <1 \\ 1+x & 1\le x \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 15
DSolve[{y'[x]==Piecewise[{{0,x<1},{1,x>=1}}],{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 2 & x\leq 1 \\ x+1 & \text {True} \\ \end {array} \\ \end {array} \]