Internal problem ID [13535]
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 (g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=3 \operatorname {Heaviside}\left (t -2\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+4*y(t)=3*Heaviside(t-2),y(0) = 0, D(y)(0) = 5],y(t), singsol=all)
\[ y \left (t \right ) = \frac {3 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )^{2}}{2}+\frac {5 \sin \left (2 t \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 37
DSolve[{y''[t]+4*y[t]==UnitStep[t-2],{y[0]==0,y'[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 5 \cos (t) \sin (t) & t\leq 2 \\ \frac {1}{4} (-\cos (4-2 t)+10 \sin (2 t)+1) & \text {True} \\ \end {array} \\ \end {array} \]