Find the general solution of the differential equations `(dy)/(dx)=sin^(-1)x`

Explanation

`(dy)/(dx)=sin^(-1)x`
`implies dy=sin^(-1)x.dx`
`implies intdy=int1*sin^(-1)xdx+x`
`impliesy=sin^(-1)x*int1dx-int((d)/(dx)sin^(-1)x)(int1*dx)dx+c`
`implies y=sin^(-1)x`
`=int(x)/(sqrt(1-x^(2)))dx+c`
Let `1-x^(2)=t`
`implies -2x=(dt)/(dx)`
`implies xdx=(-dt)/(2)`
`implies y=xsin^(-1)x-int(-dt)/(2sqrt(t))+c`
`impliesy=xsin^(-1)x+(1)/(2)intt^(-1//2)dt+c`
`implies y=x sin^(-1)x+sqrt(t)+c`
`implies y=x sin^(-1)x+sqrt(1-x^(2))+c`