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 ^{-1} x)^{2}+A(cos ^{-1} x)+B`


`Rightarrow frac{d y}{d x}=2(sin ^{-1} x) frac{1}{sqrt{1-x^{2}}}+A frac{-1}{sqrt{1-x^{2}}}`


`Rightarrow sqrt{1-x^{2}} y_{1}=2(sin ^{-1} x)-A`


`Rightarrow sqrt{1-x^{2}} y_{2}+y_{1} cdot frac{1}{2 sqrt{1-x^{2}}}(-2 x)=frac{2}{sqrt{1-x^{2}}}`


`Rightarrow(1-x^{2}) y_{2}-x y_{1}=2`