Find the particular solution of `cos((dy)/(dx))=a`, given that `y=2` when `x=0`

Find the particular solution of e^(dy/dx)=x+1 , given that when x=0,y=3 .

Solve the following differential equations : Find the particular solution of : (dy)/(dx)=cos(x+y+2) , given that x=0, y=-2 .

Find the particular solution of (dy)/(dx)=cos (x+y+1) , given that x=0, y=-1 .

Find the particular solution of the following : (dy)/(dx)= y tan x , given that y=1 when x=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 this differential equation (x^(2)dy)/(dx)-xy=1+cos((y)/(x)),x!=0 Find the particular solution of this differential equation,given that when x=1,y=(pi)/(2)

For the differential equation, find the particular solution (dy)/(dx) = ( 4x + y + 1), when y =1, x =0

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 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.