Internal problem ID [13888]
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 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\operatorname {Heaviside}\left (-10+t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.859 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+9*y(t)=Heaviside(t-10),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \operatorname {Heaviside}\left (t -10\right ) \sin \left (\frac {3 t}{2}-15\right )^{2}}{9} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 26
DSolve[{y''[t]+9*y[t]==UnitStep[t-10],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {2}{9} \sin ^2\left (15-\frac {3 t}{2}\right ) & t>10 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]