Answer:
(a) y = ¼ sin(x² + C)
(b) y = ¼ sin(x²)
Step-by-step 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)
