4 years ago

Which graph represents the function?

Mathematics

1 answer:

mario62 [17]4 years ago

3 0

For this function we can find y-intercept.
x=0, y=-2
This graph is on the top, right.

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A. Solve the differential equation <img src="https://tex.z-dn.net/?f=y%27%3D2x%20%5Csqrt%7B1-y%5E2%7D%20" id="TexFormula1" title

kirill [66]

$y' = \frac{dy}{dx}$

seperable differential equations will have the form
$\frac{dy}{dx} = F(x) G(y)$

what you do from here is isolate all the y terms on one side and all the X terms on the other
$\frac{dy}{G(y)} = F(x) dx$
just divided G(y) to both sides and multiply dx to both sides

then integrate both sides
$\int \frac{1}{G(y)} dy = \int F(x) dx

$

once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it

In your problem,
$G(y) = \sqrt{1-y^2}

F(x) = 2x$

so all you need to integrate is
$\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx$