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.
