Find the particular solution of the differential equation `dy/dx = 1+x+y+xy`, given that y=0 when x=1

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

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

Find the particular solution of the differential equation log ((dy)/(dx))=3x+4y given that y = 0 when x = 0 .

Find the particular solution of the differential equation (dy)/(dx)=-4x y^2 given that y=1,w h e nx=0.

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 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.

Find the particular solution of the differential equation (dy)/(dx)=(x y)/(x^2+y^2) given that y=1\ w h e n\ x=0.

Find the particular solution of the differential equation (1-y^2)(1+logx)dx+2x ydy=0, given that y=0 when x=1.

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

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