This is what I tried
I know its periodic so I simply assumed that solution is x=Acos(wt) then I took the first and second derivatives for x' and x"
then I simply plugged those back into the equation keeping in mind that I have cos^3 term for x^3
using a trig identity I solved for it and...
I think I figured it out
the basis of L; P2-> P2 is of course (1, x, x^2)
Then you would simply take the basis and plug it back into the Linear transformation
for example L(x)= 0 (since it's the second derivate) + (x-1) - 4x
and from that point on you could find the matrix, bases of...
Homework Statement
a block of mass m rests on a horizontal frictionless surface. The block is attached to a horizontal spring.
The spring is not ideal. The force exerted on the block by the spring is F= -kx-Bx^3 where B is a positive constant.
Calculate the first-order (largest...
they don't define what p is. I assume that we need to solve for a p by solving for the homoegenous solution.
Thanks for the tips guys. I think this might point me in the right direction
First off I am NOT asking you to solve this for me. I'm just trying to understand the concept behind this problem.
Let L be a linear transformation defined by
L[p]=(x^2+2)p"+ (x-1)p' -4p
I have not seen linear transformations in this format. Usually I see something like L(x)=x1b1+ x2b2...