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DIA [1.3K]
3 years ago
7

Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared .

Mathematics
1 answer:
MatroZZZ [7]3 years ago
4 0

Answer:

1. y = sin(x²+C)

2. see below

Step-by-step explanation:

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

separation of variables

\frac{dy}{\sqrt{1-y^2} } = 2xdx

integration both sides\int\frac{dy}{\sqrt{1-y^2} } = \int2xdx

you should get :

sin^{-1} (y) = x^2+C remember constant of integration!!

2. y = sin(x²+C)

3 = sin(0+C)

y(0) = 3 does not have a solution because our sin graph is not shifted vertically or multiplied by a factor whose absolute value is greater than 1, so our range is [-1,1] and 3 is not part of this range

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Greetings!

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