A. solve differential equa y' = 4x square root (1-y^2)

b. explain why the intial val prob y' = 4x square root 1-y^2) with y (0) = 4 doesn't have solution

Step-by-step explanation:

a)

dy/dx = 4x √ (1 - y²)

Separate the variables:

dy / √ (1 - y²) = 4x dx

Integrate:

sin⁻¹ y = 2x² + C

Solve for y:

y = sin (2x² + C)

b)

Plug in initial value.

4 = sin (0 + C)

Sine cannot be greater than 1, so there is no solution.