Question

please help!
Solve the differential equation y prime equals the product of 6 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 6 times x and the square root of the quantity 1 minus y squared with y(0) = 2 does not have a solution.

Answer 1

I'd suggest you rewrite y' as (dy/dx).

Next, think about how you'd separate this equation according to variables: all the y terms on one side, all the x terms on the other.

Answer 2

ok so it would be :
dy/ \[\sqrt{1-y^2}\] = 6xdx

Answer 3

Very good. How would y ou integrate that?

\[\frac{ 1 }{ \sqrt{1-x^2} }\] Integrates very nicely, as does 6x.

Answer 4

sin^-1(x) + c?

Answer 5

Yes, the inverse sine of x plus C; this makes up the left side of your equation. What about the right side? Integrate 6x with respect to x.

Note that you need only one constant, C, in your equation.