Solve `e^(dy//dx)=x+1,` given that when x=0,y=3.

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

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

Solve (dy)/(dx)+2y=cos x.

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

(dy)/(dx) = y tan x, y = 1 when x = 0

Find a particular solution of the differential equation (x - y)(dx + dy) = dx - dy given that y = -1, when x = 0.(Hint : put x - y = t)

Find a particular solution of the differential equation (dy)/(dx) + y cot x = 4x cosec x ( x ne 0) , given that y = 0 when x = (pi)/(2) .

x(x^(2) - 1)(dy)/(dx) = 1, y = 0 when x = 2.

2xy + y^(2) - 2x^(2)(dy)/(dx) = 0, y = 2 when x = 1