`(x^2+1)(d y)/(d x)=x y`

Which of the following differential equations has y = x as one of its particular solution? (A) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=x (B) (d^2y)/(dx^2)+x(dy)/(dx)+x y=x (C) (d^2y)/(dx^2)-x^2(dy)/(dx)+x y=0 (D) (d^2y)/(dx^2)+x(dy)/(dx)+x y=0

If y= ( tan^(-1) x)^2 , show that (1+ x^2 )( d^2 y)/(d x^2 ) + 2x(1+ x^2 ) (dy/dx) -2 = 0

If y= cos (m sin^(-1) x), show that (1- x^2 )( d^2 y)/(d x^2 ) - x(dy/dx) + m^2 y = 0

If y= sin(m cos^(-1) x), then show that (1- x^2 )( d^2 y)/(d x^2 ) - x dy/dx + m^2 y =0

If y= (sin^(-1) x)^2 , then (1-x^2) (d^2 y)/(dx^2) - x (dy/dx) = ..........

If y=cos (mcos ^(-1) x ),then (1-x^(2)) (d^(2)y)/(dx^(2) )-x( dy)/(dx)=

Find the order and degree, if defined, of each of the following differential equations: i) (d y)/(d x)-cos x=0 ii) x y( (d^2 y)/(d x^2))+x((dy)/(dx))^2-y (dy)/(dx)=0 iii) y'''+y^2+e^y=0

If y= cos(m cos^(-1) x), then show that (1- x^2 ) ( d^2 y)/(d x^2 ) - x(dy/dx) + m^2 y =0