73.1.43 problem 2.9 a

Internal problem ID [15021]
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 : Tuesday, January 28, 2025 at 07:27:41 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*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 9

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

\[ y(x)\to x \theta (x) \]