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Andreyy89
4 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]4 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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