3 years ago

if we have 10 slices of sandwiches and each 2 person take one how many slices do we still have..its easy

Mathematics

1 answer:

Inessa [10]3 years ago

7 0

So easy so easy so easy so easy so easy so easy so easy 9

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Consider the system of differential equations dx/dt=−2y dy/dt=−2x. . Convert this system to a second order differential equation

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Answer:

Step-by-step explanation:

we have the following differential equations

$\frac{dx}{dt}=-2y\\\frac{dy}{dt}=-2x\\$

by differentiating the second equation we have

$\frac{d}{dt}(\frac{dy}{dt})=-2\frac{dx}{dt}\\\frac{d^{2}y}{dt^{2}}=-2\frac{dx}{dt}\\\frac{dx}{dt}=\frac{-1}{2}\frac{d^{2}y}{dt^{2}}$

and we replace dx/dt in the first equation

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and by using the characteristic polynomial

$m^{2}+4=0\\m=\±2i$

the solution is

$y(t)=Acos(2t)+Bsin(2t)$

and to compute x(t) we have

$\frac{dx}{dt}=-2Acos(2t)-2Bsin(2t)\\\\\int dx = \int[-2Acos(2t)-2Bsin(2t)]dt\\\\x(t)=-Asin(2t)+Bcos(2t)$

and if we use x(0)=4 and y(0)=3, we can calculate the constants A and B

$x(0)=B=4\\y(0)=A=3$

I hope this is useful for you

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if we have 10 slices of sandwiches and each 2 person take one how many slices do we still have..its easy​

if we have 10 slices of sandwiches and each 2 person take one how many slices do we still have..its easy