Question

Solve the differential equation y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared.
b. Explain why the initial value problem y prime equals the product of 4 times x and the square root of the quantity 1 minus y squared with y(0) = 4 does not have a solution.

Answer 1

\(y' = 4 \sqrt{1 - y^2}\)

so

\(\int \dfrac{dy}{4 \sqrt{1 - y^2}} = \int dx \)

do you mean that, or summat altogether different?

Answer 2

yes that

Answer 3

from there, it's easy