Internal problem ID [12920]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 6. Laplace transform. Section 6.6. page 624
Problem number: 6.
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 ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+4*y(t)=sin(2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y = \frac {\sin \left (2 t \right )}{8}-\frac {t \cos \left (2 t \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 21
DSolve[{y''[t]+4*y[t]==Sin[2*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} (\sin (2 t)-2 t \cos (2 t)) \]