Chapter 8: Ordinary Differential Equations

Find the general solutions of the following equations and compare computer solutions.

$y^{\text{'}\text{'}\text{'}}+y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$y"-4y\text{'}+4y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$y"+9y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$y^{\text{'}\text{'}}+2y^{\text{'}}+2y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$\left(D^2-2D+1\right)y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$\left(D^2+16\right)y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$\left(D^2-5D+6\right)y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.

$D(D+5)y=0$

Solve the following differential equations by the methods discussed above and compare computer solutions.$\left(D^2-4D+13\right)y=0$

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

$\mathit{y}\mathbf{"}\mathbf{+}\mathit{y}\mathbf{=}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{t}\mathbf{,}\mathbf{}\mathbf{3}\mathit{t}\mathbf{=}\mathbf{0}\mathbf{,}\mathit{y}{\mathbf{\text{'}}}_{\mathbf{0}}\mathbf{=}\mathbf{-}\frac{\mathbf{1}}{\mathbf{2}}$,