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

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

Find the particular solution of the differential equation : (xdy - y dx) y sin((y)/(x)) = (y dx + x dy) x cos ((y)/(x)) , given that y = pi when x = 3.

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

Solve (dy)/(dx)+3y =e^(-2x) .

Solve (dy)/(dx)+(y)/(x)=log x.

Solve (x+y)^(2)(dy)/(dx)=a^(2)