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′=49y,y′=−81x.

So far I have that
x''=49(-81x)
x''-3969x=0
r^2=3969
r=63t
A cos (63t)+Bsin(63t)

I'm not certain I'm doing this correctly so thank you for your time.

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′=49y,y′=−81x.

So far I have that
 x''=49(-81x)
 x''-3969x=0
r^2=3969
r=63t
A cos (63t)+Bsin(63t)

I'm not certain I'm doing this correctly so thank you for your time.

goformit100 · Answer

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