Find the differential equation of `xy = ae^x + be^(-x)`.

y = ae^(3x) + be^(-2x)

Find the equation of a curve passing through the point (0,0) and whose differential equation is y' = e^(x) sin x .

The general solution of the differential equation e^(x) dy + (y e^(x) + 2x)dx = 0 is

The general solution of the differential equation (dy)/(dx) = e^(x + y) is

Find order and degree of given differential equation y' + y = e^(x)

Find the general solution of the differential equation x (dy)/(dx) + 2y = x^(2)(x ne 0) .

Find the equation of the curve passing through the point (1,1) whose differential equation is x dy = (2x^(2) + 1) dx(x ne 0) .

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