Internal problem ID [2356]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-7 \sin \left (4 t \right )-14 \cos \left (4 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.025 (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)
\[ y \relax (t ) = -16 \left (\cos ^{4}\relax (t )\right )+\left (-8 \sin \relax (t )+12\right ) \left (\cos ^{3}\relax (t )\right )+\left (8 \sin \relax (t )+16\right ) \left (\cos ^{2}\relax (t )\right )+\left (4 \sin \relax (t )-9\right ) \cos \relax (t )-2 \sin \relax (t )-2 \]
✓ Solution by Mathematica
Time used: 0.286 (sec). Leaf size: 50
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]
\begin{align*} y(t)\to \frac {1}{8} \left (11 \sqrt {2} \sin \left (2 \sqrt {2} t\right )+22 \cos \left (2 \sqrt {2} t\right )-7 (\sin (4 t)+2 \cos (4 t))\right ) \\ \end{align*}