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Question

The equation of the curve passing through the origin and satisfying the equation (1+x2)dydx+2xy=4x2 is


A

3(1+x2)y=4x3

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B

3(1x2)y=4x3

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C
3(1+x2)=x3
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D

None of these

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Solution

The correct option is A

3(1+x2)y=4x3


dydx+2x1+x2y=4x21+x2
It is linear equation of the form dydx+Py=Q
Here P=2x1+x2 and Q=4x21+x2
I.F.e 2x1+x2dx=elog(1+x2)=(1+x2)
Therefore, solution is given by
y.(1+x2)=4x21+x2(1+x2)dx+c
=4x33+c.
But it passes through (0,0) therefore c = 0,
Hence the curve is 3y(1+x2)=4x3.


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