Internal problem ID [2865]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for
10.4. page 689
Problem number: Problem 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=7 \sin \left (4 t \right )+14 \cos \left (4 t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 29
dsolve([diff(y(t),t$2)+9*y(t)=7*sin(4*t)+14*cos(4*t),y(0) = 1, D(y)(0) = 2],y(t), singsol=all)
\[ y \left (t \right ) = 2 \sin \left (3 t \right )+3 \cos \left (3 t \right )-\sin \left (4 t \right )-2 \cos \left (4 t \right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 49
DSolve[{y''[t]+8*y[t]==7*Sin[4*t]+14*Cos[4*t],{y[0]==1,y'[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (-7 \sin (4 t)+11 \sqrt {2} \sin \left (2 \sqrt {2} t\right )-14 \cos (4 t)+22 \cos \left (2 \sqrt {2} t\right )\right ) \]