Mathematics: A. solve the differential equation . b. explain why the initial value problem with y(0) = 3 does not have a solution.

A. solve the differential equation . b. explain why

Ответ:

derick5977

17.01.2022

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

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
$\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx$

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Ответ:

niyag2gi

21.04.2021

Mathematics

468

Step-by-step explanation:

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A. solve the differential equation .
b. explain why the initial value problem with y(0) = 3 does not have a solution.

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