Solve the differential equation y prime equals the product of 6 times x and the square root of the quantity 1 minus y squared.

Question

1. Solve the differential equation .
2. Explain why the initial value problem  with y(0) = 2 does not have a solution.

Answer 1

Am I missing something?

dy/dx = 6xsqrt(1-y²) has a solution...variables are separable:

dy/sqrt(1-y²) = 6x dx

arcsin y = 3x² + C

y = sin (3x² + C)

Since y(0) = sin C, the initial value cannot be 2.