Internal problem ID [13223]
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 6.3 page 600
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+4 y=8} \] With initial conditions \begin {align*} [y \left (0\right ) = 11, y^{\prime }\left (0\right ) = 5] \end {align*}
✓ Solution by Maple
Time used: 4.797 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+4*y(t)=8,y(0) = 11, D(y)(0) = 5],y(t), singsol=all)
\[ y \left (t \right ) = 9 \cos \left (2 t \right )+\frac {5 \sin \left (2 t \right )}{2}+2 \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 19
DSolve[{y''[t]+4*y[t]==8,{y[0]==11,y'[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 9 \cos (2 t)+5 \sin (t) \cos (t)+2 \]