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Andreyy89
3 years ago
14

Find the solution of the system x′=−4y,y′=−2x, where primes indicate derivatives with respect to t, that satisfies the initial c

ondition x(0)=−2,y(0)=−2.
Mathematics
1 answer:
Andreas93 [3]3 years ago
5 0

Answer:2y^2 = x^2+4

Step-by-step explanation:

given is a differntial equation in parametric form as

x'=-4y\\y'=-2x

We can find dy/dx by dividing y' by x'

\frac{dy}{dx} =\frac{-2x}{-4y} \\4ydy =2x dx\\2y^2 = x^2+C

(By separating the variables and integrating)

C is arbitrary constant

When x=-2, y =-2

Substitute to get

8=4+C\\C=4

So solutoin is

2y^2 = x^2+4

is the solution

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3 years ago
Sun, a kayaker, paddles 8 miles upstream (against the current) in 2 hours. Returning to her original location, she paddles downs
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4 0
2 years ago
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
MA_775_DIABLO [31]

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2 years ago
A math teacher gets a starting salary of $30,000. IF she gets a 1.5% increase in salary each year, what will her total income be
kolezko [41]
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2 years ago
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4 0
3 years ago
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