`(1+2x)dy-(1-2y)dx=0`, का हल क्या है ?

Options

A. `x-y-2xy=C`
B. `y-x-2xy=C`
C. `y+x-2xy=C`
D. `x+y+2xy=C`

Answer

A

Explanation

दिया है,
`(1+2x)dy-(1-2y)dx=0`
`(1+2x)dy=(1-2y)dx`
`rArr (dy)/(1-2y)=(dx)/(1+2x)`
समाकलन करने पर,
`rArr-(1)/(2)log(1-2y)=1/2log(1+2x)+C'`
`rArr log(1+2x)+log(1-2y)=-2C'`
`rArr log(1+2x)(1-2y)=-2C'`
`rArr(1+2x)(1-2y)=e^(-2)C'`
`rArr 1-2y+2x-4xy=e^(-2)C'`
`rArr2x-2y-4xy=e^(-2)C'-1`
`rArrx-y-2xy=1/2(e^(-2)C'-1)`
`rArrx-y-2xy=C` [ जहाँ `C=1/2(e^(-2)C'-1)`]