Third Order Homogeneous Linear Differential Equation

yaarpatandar

New member
Joined
Nov 9, 2016
Messages
1
Give an example of a third order homogeneous linear differential equation such that the functions y1=2, y2=e-x, and y3=e2x are its solutions. Justify your claim.


I have no idea on how to do this.
 
Give an example of a third order homogeneous linear differential equation such that the functions y1=2, y2=e-x, and y3=e2x are its solutions. Justify your claim.


I have no idea on how to do this.
.

Can you do the following:


Give an example of a second order homogeneous linear differential equation such that the functions y1=e-x & y2=e2x are its solutions.
 
A "third order homogeneous linear differential equation" (with constant coefficients) is of the form ay'''+ by''+ cy'+ dy=0. It has "characteristic equation" \(\displaystyle at^3+ br^2+ cr+ d= 0\)". If r= a is a real root, then (r- a) is a factor of that polynomial and \(\displaystyle Ce^{ax}\) is a solution to the differential equation.

Here you are told that solutions are 2 (\(\displaystyle = 2e^{0x}\)), \(\displaystyle e^{-x}\), and \(\displaystyle e^{2x}\) so r= 0, -1, and 2.
 
Top