Find the general solution of y''' + 9y'' + y' − 111y = 0 if it is known that y1 = e−6x cos(x) is one solution.

Step-by-step explanation:

The objective of this question is to solve:

Suppose the general solution is proportional to for is constant; Then:

Let's replace into the above equation:

i.e.

To Replace:

with

Thus;

+ + - 111 = 0

∴

In as much as for any finite ; Then:

By Factorization:

However;

The root yield;

The root yield;

∴

The general solution is:

Using Euler's Identity ;

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

step-by-step explanation: i dont