" (ii) "x^(2)(1-y)(dy)/(dx)+y^(2)(1+x)=0quad " [UP "2

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

If (1+x^(2))(dy)/(dx)=1+y^(2),y(0)=1, then y(2)=

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

if y=x^(x), then prove (d^(2)y)/(dx^(2))-(1)/(y)((dy)/(dx))^(2)-(y)/(x)=0

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

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

If y=log[x+sqrt(x^(2)+1)] , then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=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

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

If y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0