Show that the differential equations (x−y)dydx=x+2y is homogeneous a

1.	Show that the differential equations (x−y)dydx=x+2y is homogeneous and solve it also. OR Find the differential equations of the family of curves (x−h)2+(y−k)2=r2, where h and k are arbitrary constants.
Answer» Show that the differential equations $(x - y) \frac{d y}{d x} = x + 2 y$ is homogeneous and solve it also. OR Find the differential equations of the family of curves $(x - h)^{2} + (y - k)^{2} = r^{2},$ where h and k are arbitrary constants.

Show that the differential equations (x−y)dydx=x+2y is homogeneous and solve it also. OR Find the differential equations of the family of curves (x−h)2+(y−k)2=r2, where h and k are arbitrary constants.

Answer»

Show that the differential equations $(x - y) \frac{d y}{d x} = x + 2 y$ is homogeneous and solve it also.

Find the differential equations of the family of curves $(x - h)^{2} + (y - k)^{2} = r^{2},$ where h and k are arbitrary constants.