Internal problem ID [13878]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 29. Convolution. Additional Exercises. page 523
Problem number: 29.6 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.782 (sec). Leaf size: 15
dsolve([diff(y(t),t$2)+4*y(t)=sin(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (t \right )}{3}-\frac {\sin \left (2 t \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 15
DSolve[{y''[t]+4*y[t]==Sin[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {1}{3} \sin (t) (\cos (t)-1) \]