Internal problem ID [13851]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page
496
Problem number: 27.1 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+3 y=\operatorname {Heaviside}\left (t -4\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.937 (sec). Leaf size: 20
dsolve([diff(y(t),t)+3*y(t)=Heaviside(t-4),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\operatorname {Heaviside}\left (t -4\right ) \left (-1+{\mathrm e}^{-3 t +12}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 27
DSolve[{y'[t]+3*y[t]==UnitStep[t-4],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{3}-\frac {1}{3} e^{12-3 t} & t>4 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]