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((dy)/(dx))^(2) + 2y cot x (dy)/(dx) = y...

`((dy)/(dx))^(2) + 2y cot x (dy)/(dx) = y^(2)` has the solution

A

`y + (c)/(1+cos x) = 0`

B

`y = (c)/(1-cos x)`

C

`x = sin^(-1) sqrt((c)/(2y))`

D

`x = cos^(-1) ((c)/(2y))`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`((dy)/(dx))^(2)+2y cot x (dy)/(dx)-y^(2)=0`
`rArr" "(dy)/(dx)=(-2y cot x +- sqrt(4y^(2)cot^(2)x+4y^(2)))/(2)`
`rArr" "(dy)/(dx)= - y(cot x +- "cosec x")dx`
`rArr" "(dy)/(y)=(-cot x +- "cosec x")dx`
`rArr" "log y = -[log sin x +- log("cosec x"+cot x)]+log c`
`=-"log"(sin x)/(c("cosec x"+- cot x))`
`="log"(c(1 +- cos x))/(sin^(2)x)`
`="log"((c)/(1 +- cos x))`
`rArr" "y=(c)/(1 +- cos x)`
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