" (1) Solue "(1+y^(2))dx-y(1+x^(2))dy=6

y(1+x^(2))dy=x(1+y^(2))dx

y(1-x^(2))dy=x(1+y^(2))dx

Solve :(1+y^(2))dx=(tan^(-1)y-x)dy

(1+x^(2))dy=y^(2)dx

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

(1+x^(2))(dy)/(dx) = 1-y

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

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

Find dy/dx if y(1-x^2)=6

Solve the following differential equations. (i) (dy)/(dx) =(1+y^(2))/(1+x^(2)) (ii) (dy)/(dx) = (sqrt(1-y^(2)))/(sqrt(1-x^(2))) (iii) (dy)/(dx) = 2y tan hx (iv) sqrt(1+x^(2))dx + sqrt(1+y^(2))dy = 0 (v) (dy)/(dy) = e^(x-y)+x^(2)e^(-y)