Compute the differential for both sides:
4y - 3xy + 8x = 0
→ 4 dy - 3 (y dx + x dy) + 8 dx = 0
Solve for dy :
4 dy - 3y dx - 3x dy + 8 dx = 0
(4 - 3x) dy + (8 - 3y) dx = 0
When x = 0, we have
4y - 3•0y + 8•0 = 0 → 4y = 0 → y = 0
and with dx = 0.05, we get
(4 - 3•0) dy + (8 - 3•0) • 0.05 = 0
→ 4 dy + 0.4 = 0
→ 4 dy = -0.4
→ dy = -0.1