Find d^2y/dx^2 in terms of x and y

x^2y^2-16x=8
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2 Answers

Please use parentheses to correctly write the equation. I would be able to assist you much better.
by Level 1 User (260 points)

Given............y.x^2.y^2 - 16x = 8

⇒x^2.y^3 -16x = 8

if f ' = dy/dx and f '' = d^2y/dx^2

then.....

2xy^3 + 3x^2.y^2.f ' - 16 = 0 .......................(1)

f ' = {16 - 2x.y^3}/3x^2.y^2........................(2)

from eqn (1)

2y^3 + 6xy^2.f ' + 6xy^2.f ' + 6yx^2.f '' = 0

f '' = -y^2/3x^2 - 2.f'

from eqn(2)

f '' = -y^2/3x^2 - 2{16 - 2xy^3}/3x^2.y^2

f '' = {4xy^3 - y^4 - 32}/3x^2.y^2

 

by Level 3 User (4.0k points)

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