Question

Solve the following system by differentiating the first equation and substituting the second to get an equation in only one variable. Primes indicate differentiation with respect to t. Use the constants A, B, etc. for any arbitrary constant(s) in your solution.
x'=16y y'=−9x

Answer 1

I really wish you would stick around after you post so I can help you in real time.

Answer 2

\[x'=16y\]\[y'=-9x\]take the derivative of the second equation wrt t and you get\[y''=-9x'\]now you can sub the expression for x' from the first equation into this last one\[y''=-9(16y)=-144y\]\[y''+144y=0\]which has the solution\[y=c_1\cos(12t)+c_2\sin(12t)\]now that we have y we can go back and solve the first equation, which is separable\[x'=\frac{dx}{dt}=16y=16c_1\cos(12t)+16c_2\sin(12t)\]\[x=16\int c_1\cos(12t)+c_2\sin(12t)dt\]\[x=\frac43[c_1\sin(12t)-c_2\cos(12t)]+c_3\]

Answer 3

Sorry I had to go to work

Answer 4

Also I go the same answer as you did but it's wrong :/

Answer 5

@lalaly DE help please :D

Answer 6

...because I am confused
I see wolfram's answer and I don't get it

Answer 7

it is reasonable that there should be no third constant, I was suspicious of that
I tried to make a matrix of it and do the eigenvalue thing , but couldn't
in short, I'm stumped

Answer 8

Nevermind! i figured it out! thank you!

Answer 9

how did you do it?

Answer 10

x'=16y x''=16y'=16(-9x)=144x

Answer 11

x''-144x=0

Answer 12

r^2-144=0
r=12t

Answer 13

plug that into the general equation for x

Answer 14

and you get Acos(12t)+Bsin(12t)

Answer 15

A and B are the same as saying c_1 and c_2

Answer 16

is that all?

Answer 17

but that is not the solution wolfram has
and that is x, what about y ?

Answer 18

for y you od the same thing with x. from the equation x'=16y you get y=x'/16
We already found that x is equal to 12 previously so no you plug it into the general equation which will giver you

Answer 19

(-12/16)Asin(12t)+(12/16)Bcos(12t)

Answer 20

and I check my answer it's correct

Answer 21

checked*

Answer 22

I did realize that answer, but it was not what wolf had
also you seem to get a different answer depending on the order in which you solve the problem
I still have quite a few questions, but congrads that you're done with it!

Answer 23

wait I'm sorry I'm confused!

Answer 24

also wolfram is not always correct it sometimes solves for something different than what you intially asked for

Answer 25

ok I get it
I swear I had that answer, but I doubted myself because it was so similar to the other (minus the extra constant), and different from wolf (which I know is frequently wrong about this kind of thing)
oh well, thanks!