Question

differential equation

Answer 1

@KendrickLamar2014

Answer 2

@ganeshie8

Answer 3

@confluxepic @Preetha

Answer 4

maybe start by solving the characteristic equation

\[r^2-\sqrt{5}=0\]

Answer 5

how

Answer 6

i am not getting it

Answer 7

what exactly are you not getting ?

Answer 8

how to substitute r^{2}

Answer 9

are you asking how i got that equation ?

Answer 10

yes

Answer 11

that is because of euler

Answer 12

let \(y = e^{rt}\) be a solution of the given differential equation

Answer 13

\(y = e^{rt}\)

\(y'' = ?\)

Answer 14

\[e ^{rtn}\]

Answer 15

Careful,

\(y' = \dfrac{dy}{dx}\)

\(y'' = \dfrac{d^2y}{dx^2}\)

Answer 16

\(y'\) is the first derivative of \(y\)

\(y''\) is the second derivative of \(y\)

Answer 17

ok

Answer 18

As I see it, you have two choices: Actually solve the D. E. (as you're trying to now), or check out each of the four given answers to determine which satisfies the given D. E.

The D. E. is \[y''-\sqrt{5}y=0\]

So, supposing we were checking out possible solution #1:
1) Find the 2nd derivative, y'', of that possible solution.
2. Substitute your result for y'' in the D. E.
3. subst. y=possible solution #1 into the D. E.
4. Determine whether or not the D. E. is true after these substitutions have been made.