Form the differential equation having `y=(sin^(-1) x)^2 +A cos^(-1) x +B` where A and B are arbitrary constants, as its general solution

Explanation

`y = (sin^-1x)^2+Acos^-1x+B`

`=>dy/dx = 2sin^-1x(1/sqrt(1-x^2))+A(-1/(sqrt(1-x^2)))`

`=>dy/dx = (2sin^-1x-A)(1/sqrt(1-x^2))`

`=>dy/dx(sqrt(1-x^2)) = (2sin^-1x-A)`

`=>A = 2sin^-1x-dy/dx(sqrt(1-x^2)) `

Again differentiating w.r.t. `x`,

`=>0 = 2(1/sqrt(1-x^2)) -dy/dx(1/(2sqrt(1-x^2)))(-2x) - sqrt(1-x^2)(d^2y)/dx^2)`

`=>2 +xdy/dx -(1-x^2)(d^2y)/dx^2 = 0`

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