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

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))

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

The solution of e^(x((y^(2)-1))/(y)){xy^(2)dy+y^(3)dx}+{ydx-xdy}=0 , is

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

Equation of curve passing through (1,1) & satisfyng the differential equation (xy^(2)+y^(2)+x^(2)y+2xy)dx+(2xy+x^(2))dy=0 is