Question

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

Answer 1

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.