solve the differential equation `(x^2-y^2) d x+2 x y d y=0`

solve the differential equation (x^2+x y) d y=(x^2+y^2) d x

Consider the differential equation (x^2-y^2)dx+2xydy=0 . Choose the correct solution from the following. For y=1 when x=1 a) x^2+y^2=-2x b) x^2+y^2=2x c) x^2+y^2-x=0 d) x^2+y^2+x=0

Solve the differential equation (x d y-y d x) y sin (y/x)=(y d x+x d y) x cos (y/x)

Solve the differential equation: [xsin^2(y/x)-y]dx+x dy=0 .

Consider the differential equation (x^2 -1)(dy)/(dx) + 2 (x + 2) y = 2(x+1) Solve the differential equation.

Solve the differential equation xdy/dx+y=1/x^2 .

Verify that the function y=acosx+bsinx is the solution of the differential equation (d^2y)/dx^2+y=0

Solve the differential equation y e^(x/y) d x=(x e^(x/y)+y^2) d y(y ne 0)

Show that the function y=Ax+B/x is a solution of the differential equation x^2(d^2y)/dx^2+xdy/dx-y=0 .

Find a particular solution of the differential equation (x-y)(d x+d y)=d x-d y , given that y=-1 , when x=0 (Hint: Put x-y=t)