Internal problem ID [13854]
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 (f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\sin \left (2 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 3.891 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+4*y(t)=sin(2*t),y(0) = 3, D(y)(0) = 5],y(t), singsol=all)
\[ y \left (t \right ) = \frac {21 \sin \left (2 t \right )}{8}-\frac {\cos \left (2 t \right ) \left (-12+t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 26
DSolve[{y''[t]+4*y[t]==Sin[2*t],{y[0]==3,y'[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {21}{8} \sin (2 t)+\left (3-\frac {t}{4}\right ) \cos (2 t) \]