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General solution of (2x-10y^(3))(dy)/(dx...

General solution of `(2x-10y^(3))(dy)/(dx)+y=0`, is

A

`2x^2 y = y^5 +C`

B

`2xy^2 = y^5 +C`

C

`xy^2 = 2y^5 + C`

D

`xy^2 = y^5 +C`

Text Solution

Verified by Experts

The correct Answer is:
C
`(2x - 10y^3) (dy)/(dx) + y =0`
`implies 2xdy + ydx = 10y^(3) dy implies 2xydy + y^(2) dx = 10y^(4) dy`
`implies d(y^(2) . x ) = 10y^(4) dy implies xy^(2) = 2y^(5) + C`
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