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

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

If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^(-1)x), show that ((1-x^2)d^(2y))/(dx^2)=x(dy)/(dx)-4y

If y=e^(msin^(-1)x) prove that (1-x^2)((d^2y)/dx^2)-x(dy)/dx=m^2y

6. (1+xy^(2))dx+(1+x^(2)y)dy=0

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y), prove that (dy)/(dx)=sqrt((1-y^2)/(1-x^2))

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

Solve the initial value problem: y-x(dy)/(dx)=2(1+x^2(dy)/(dx)),\ y(1)=1

The solution of differential equation (1-xy + x^(2) y^(2))dx = x^(2) dy is

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))

If sqrt(1-x^2) + sqrt(1-y^2)=a(x-y) , prove that (dy)/(dx)= sqrt((1-y^2)/(1-x^2))