1.

The solution of the DE ` (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))) = 0 ` isA. `"sin"^(-1)x."sin"^(-1)y=C`B. `"sin"^(-1)x=C"sin"^(-1)y`C. `"sin"^(-1)x-"sin"^(-1)y=C`D. `"sin"^(-1)x+"sin"^(-1)y=C`

Answer» Correct Answer - D
We have `(dy)/(dx) +sqrt(1-y^(2))/(sqrt(1-x^(2))) = 0`
`(dy)/(dx) =-sqrt(1-y^(2))/(1-x^(2))`
`int (dy)/(sqrt(1-y^(2)))=-int (dx)/(sqrt(1-x^(2)))`
`"sin"^(-1) "("xsqrt(1-y^(2))+ysqrt(1-x^(2))")"=C`
`xsqrt(1-y^(2))+ysqrt(1-x^(2))=C`


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