[" (34) "s*T" the "D*Equad x(dy)/(dx)sin((y)/(x))+x-y sin((y)/(x))=0],[" is a homogenous.Find its partecelan solution "],[" when "x=1,y=pi/2]

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 x sin ((y)/(x))(dy)/(dx) = y sin ((y)/(x)) + x is homogeneous. Also find its general solution.

Show that the differential equation x sin ((y)/(x))(dy)/(dx) = y sin ((y)/(x)) + x is homogeneous. Also find its general solution.

Find (dy)/(dx) when : (cos x)^(y)=(sin y)^(x)

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.

Solution of the differential equation (x(dy)/(dx)-y)sin((y)/(x))=x^(2)e^(x) is

Show that the differential equation 2y e^(x/y)dx+(y-2x e^(x/y))dy=0 is homogeneous and find its particular solution, given that, x" "=" "0 wheny" "=" "1 .