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Question

Find the Differential Equation whose solution is a2y-ax+8=0.


A

8y21+y+xy1=0

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B

8y21+y-xy1=0

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C

8y21-y-xy1=0

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D

8y21-y+xy1=0

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Solution

The correct option is B

8y21+y-xy1=0


Explanation for the correct option:

Find the required differential equation.

The solution of the required differential equation is given as,

a2y-ax+8=0.....(1)

differentiate equation (1) with respect tox we get,

a2dydx-ad(x)dx+8=0dydxa2-a×1+0=0dydxa2-a=0a2y1-a=0dydx=y1a(ay1-1)=0

So, a=0 and a=1y1

a=0 is not possible as the value of the arbitrary constant can not be 0.

Therefore, a=1y1

By putting the value of a in equation (1) we get,

yy12-xy1+8=0

By multiplying y12both sides,

yxy1+8y12=0


8y12+yxy1=0

Hence, option (B) is the correct answer.


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