Question

How do you do this question?

Answer 1

(a) y = ¼ sin(x² + C)

(b) y = ¼ sin(x²)

Explanation:

(a) dy/dx = ½ x √(1 − 16y²)

dy / √(1 − 16y²) = ½ x dx

4 dy / √(1 − 16y²) = 2x dx

sin⁻¹(4y) = x² + C

4y = sin(x² + C)

y = ¼ sin(x² + C)

(b) When x=0, y=0.

0 = ¼ sin(C)

C = 0

y = ¼ sin(x²)