AME 301 Homework 1

B. Goodwine
J. Lucey
Fall, 2003

Issued: August 29, 2003
Due: September 3, 2003

For each of the following equations, identify them as

If the differential equation is a linear, homogeneous, constant coefficient ordinary differential equation, determine its solution (5 points).

$\begin{eqnarray*} 5 \ddot x + 6 \dot x + \sin(t) x &=& \cos(t^2)\\ x(0) &=& 1 \\ \dot x(0) &=& \pi. \end{eqnarray*}$
$\begin{eqnarray*} 2 \ddot x + 19 \dot x + 24 x &=& 0\\ x(0) &=& 1\\ \dot x(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 2 \frac{\partial^2 \zeta}{\partial \gamma^2} + 19 \frac{\parti... ...&=& \gamma^2 + \alpha^2\\ \zeta(0) &=& 1\\ \dot \zeta(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 6 \ddot x + 23 \dot x + x^3 &=& \sin(t^2)\\ x(0) &=& 1\\ \dot x(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 6 \ddot x + 23 \dot x + t^3 x^2 &=& 0\\ x(0) &=& 1\\ \dot x(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 6 \ddot x + 23 \dot x + t^3 x &=& \sin(t^2)\\ x(0) &=& 1\\ \dot x(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 2 \frac{d^2 \xi}{d \eta^2} + 19 \frac{d \xi}{d \eta} + 24 \xi &=& 0\\ \xi(0) &=& 1\\ \dot \xi(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 6 \ddot x + 23 \dot x + 3^2 x &=& \sin(t^2)\\ x(0) &=& 1\\ \dot x(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} \pi \ddot x + e \dot x + x &=& 0\\ x(0) &=& 1\\ \dot x(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 2 \frac{d^2 \zeta}{d \gamma^2} + 19 \frac{d \zeta}{d \gamma} + 24 \zeta &=& 0\\ \zeta(0) &=& 1\\ \dot \zeta(0) &=& 0 \end{eqnarray*}$
$\begin{eqnarray*} 2 \frac{d^2 \zeta}{d \gamma^2} + 19 \frac{d \zeta}{d \gamma} +... ...4 \zeta &=& \sin \gamma\\ \zeta(0) &=& 1\\ \dot \zeta(0) &=& 0 \end{eqnarray*}$

Last updated: August 29, 2003.
B. Goodwine (goodwine@controls.ame.nd.edu)