Write a 6th order homogeneous linear equation whose general solution is
y=c1+c2e-t+c3cos(3t)+c4sin(3t)+c5tc os(3t)+c6tsin(3t)

Step-by-step explanation:

We are given that  a general solution of 6th order homogeneous linear equation

We have to find the 6th order homogeneous linear differential equation whose general solution is given above.

We know that imaginary roots are in pair

There two values of imaginary roots and the values of imaginary roots are repeat.

From first term of general solution we get D=0

From second term of general solution we get D=-1

Last four terms are the values of imaginary roots and roots are repeated.

Therefore, D= and D=

Substitute all values then we get

Therefore, the 6th order homogeneous linear differential equation is

if the pizza is divided equally into 2 equal halves then you would get

πr^2/2

where r is the radius of the pizza.

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there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."