Question

12. Given e-xy – 4xy = 0, dy can be proved to be
a)-y/x
b) y/x
c) x/y
d) none of these​

Answer 1

Correct answer is option 'A

Explanation:

Given, e^{-xy} - 4xy = 0

difference with respect to x

e^{-xy}[d(-xy)/dx ] - 4[ydx/dx + xdy/dx ] = 0

e^{-xy}[ -ydx/dx - xdy/dx] - 4[y + xy'] = 0 [ ∵ dy/dx = y' ]

e^{-xy}[-y - xy'] - 4[y + xy'] = 0

[y + xy'][e^{-xy} + 4] = 0

y + xy' = 0 because e^{-xy} + 4 ≠ 0

y' = -y/x