Internal problem ID [13285]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 13
dsolve([diff(y(x),x)=piecewise(x<0,0,x>=0,1),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left \{\begin {array}{cc} 0 & x <0 \\ x & 0\le x \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 9
DSolve[{y'[x]==UnitStep[x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \theta (x) \]