हल कीजिए-
`x(x^(2)-1)(dy)/(dx)=1,y =0` जब `x=2.`

x(2y-1)dx+(x^(2)+1)dy=0

(1+x^(2))dx+(1+y^(2))dy=0

2 x y+y^2-2 x^2 (dy)/(dx)=0 , y=2 when x=1

(1+x^(2))(dy)/(dx)+2xy=(1)/(1+x^(2));y=0 if x=1

(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 when x= 1

(1 + x^(2))(dy)/(dx) + 2xy = (1)/(1 + x^(2)), y = 0 when x= 1

x(1+y^(2))dx+y(1+x^(2))dy=0 at (0, 0)

Solve the following differential equations (i) (1+y^(2))dx = (tan^(-1)y - x)dy (ii) (x+2y^(3))(dy)/(dx) = y (x-(1)/(y))(dy)/(dx) + y^(2) = 0 (iv) (dy)/(dx)(x^(2)y^(3)+xy) = 1

If y=log (x + sqrt(x^(2) + 1)) then show that, (x^(2) + 1) (d^(2)y)/(dx^(2)) + x (dy)/(dx)= 0