Internal problem ID [13885]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 30. Piecewise-defined functions and periodic functions. Additional Exercises.
page 553
Problem number: 30.6 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\operatorname {Heaviside}\left (-3+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 3.656 (sec). Leaf size: 14
dsolve([diff(y(t),t)=Heaviside(t-3),y(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {Heaviside}\left (t -3\right ) \left (t -3\right )+4 \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 15
DSolve[{y'[t]==UnitStep[t-3],{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 4 & t\leq 3 \\ t+1 & \text {True} \\ \end {array} \\ \end {array} \]