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The solution of ((dy)/(dx))^(2)-2(x+(1)/...

The solution of `((dy)/(dx))^(2)-2(x+(1)/(4x))(dy)/(dx)+1=0`

A

`y = x^(2) + c`

B

`y = (1)/(2) In (x) + c, x gt 0`

C

`y = (x)/(2) + c`

D

`y = (x^(2))/(2) + c`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`rArr" "((dy)/(dx))^(2)-3(x+(1)/(4x))(dy)/(dx)+1 = 0`
`rArr" "((dy)/(dx)-2x)((dy)/(dx)-(1)/(2x))=0`
`therefore" "dy = 2x dx or dy=(1)/(2x)dx`
`rArr" "y=x^(2)+ c or y = (1)/(2)"In x"+c, x gt 0`.
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