Question

A) Find dy for 4y - 3xy + 8x = 0 and b) evaluate dy for x = 0 and dx = 0.05

Answer 1

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