If`y=(sin^(-1)x)^2` ,prove that `(1-x^2)y_2-x y_1-2=0.`

1.	If`y=(sin^(-1)x)^2` ,prove that `(1-x^2)y_2-x y_1-2=0.`
Answer» `y_1=dy/dx=2sin^(-1)x1/sqrt(1-x^2)=(2sin^(-1)x)/sqrt(1-x^2)` `y_1=(d^2y)/(dx^2)=2[1/(1-x^2)-1/2sin^(-1)x(1-x^2)^(-3/2)*(-2)]/(1-x^2)` `y_2=2/(1-x^2)+(2sin^(-1)x)/(1-x^2)^(3/2)` `(1-x^2)y_2-xy_1` `2+(2sin^(-1)x)/(1-x^2)^(1/2)-(2sin^(-1)x)/(1-x^2)^(1/2)=2`

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