Question #d59b8

1 Answer
Nallasivam V
Aug 22, 2017

#(d^2y)/(dx^2)=(2y)/(5x+2y)#

Explanation:

Given -

#x^2y+xy^2=2#

Use the product rule to differentiate the terms #x^2y, xy^2#

When you differentiate #x^2y#
Keep #y# as constant and differentiate #x^2 #

The differentiate #y# and keep #x^2#constant.

Do the same for the other terms and in subsequent differentation.

#2xy +dy/dxx^2+y^2+dy/dx2xy=0#

#2y+(d^2y)/(dx^2)x+(d^2y)/(dx^2)2x+(d^2y)/(dx^2)2y+(d^2y)/(dx^2)2x=0#

#(d^2y)/(dx^2)x+(d^2y)/(dx^2)2x+(d^2y)/(dx^2)2y+(d^2y)/(dx^2)2x=2y#
#(d^2y)/(dx^2)(x+2x+2y+2x)=2y#
#(d^2y)/(dx^2)(5x+2y)=2y#
#(d^2y)/(dx^2)=(2y)/(5x+2y)#

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