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

Solve the following differential equation: y^(2)(dy)/(dx)+x-(1)/(y)=0

If y=sqrt(x+1)-sqrt(x-1) , prove that (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-(1)/(4)y=0 .

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

Find the particular solution of y(1-x^2)(dy)/(dx)+x(1-y^2)=0 , given that y=0 when x=0

If y=sqrt(x+1)-sqrt(x-1) , then prove that (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx)-1/4y=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-1)/(y))(dy)/(dx)=0

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

(1+x+xy^(2))(dy)/(dx)+(y+y^(3))=0