Y"+4y = 8 sin 2x. trial solution using annihilator technique
linear algebra and differential equations
i am so confused why would you multiple by x up(x)

A second order linear, non - homogeneous ODE has a form of

The general solution to,

Can be written as,

Where is a solution to the homogeneous ODE and the particular solution, function that satisfies the non - homogeneous equation.

We can solve by rewriting the equation,

Which simplifies to,

From here we get two solutions,

So the form here refines,

The same thing we do with to get form of,

From here the final form emerges,

Hope this helps.

r3t40

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

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.