Show that the differential equation `x(dy)/(dx)sin(y/x)+x-ysin(y/x)=0` is homogenous. Find the particular solution of this differential equation, given that `x=1` when `y=pi/2`.

Show that the differential equation xdy/dxsin(y/x) +x-y sin (y/x) =0 is homogeneous. Find the particular solution of this differential equation, given that x = 1 when y=π\2

Show that the differential equation 2y e^(x/y)\ dx+(y-2x e^(x/y)) dy=0 is homogeneous. Find the particular solution of this differential equation, given that x=0 when y=1.

Show that the differential equation 2ye^((pi)/(y))dx+(y-2xe^(xy))dy=0 is homogeneous.Find the particular solution of this differential equation,given that x=0 when y=1.

Show that the differential equation 2y e^(x/y)\ dx+(y-2x e^(x/ y) ) dy=0 is homogeneous. Find the particular solution of this differential equation, given that x=0 when y=1.

Show that the differentia equation (xe^(y//x) + y) dx = x dy is homogeneous. Find the particular solution of this differential equation, given that x = 1 when y = 1.

Show that the differential equation [x sin^(2)((y)/(x)) - y]dx+x dy = 0 is homogeneous. Find the particular solution of this differential equation, given that y = (pi)/(4) when x = 1.

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

Find the particular solution of the differential equation (dy)/(dx)=3x , given that y = 0 when x = 0 .

Find the particular solution of the differential equation (dy)/(dx)=-4xy^(2) given that y=1, when x=0