Internal problem ID [5937]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 7 THE LAPLACE TRANSFORM. 7.4.1 DERIVATIVES OF A TRANSFORM.
Page 309
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-\cos \left (3 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+9*y(t)=cos(3*t),y(0) = 2, D(y)(0) = 5],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (10+t \right ) \sin \left (3 t \right )}{6}+2 \cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 23
DSolve[{y''[t]+9*y[t]==Cos[3*t],{y[0]==2,y'[0]==5}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{6} (t+10) \sin (3 t)+2 \cos (3 t) \\ \end{align*}