Hi, I would be really grateful to anyone who may help with this...
I need to find the general solution for the differential equation
dy/dx = (cos x - sin x)e^cos x + sin x - y
(giving the solution in implicent form)
I have differentiate the function f(x) = e^cos x + sin x using the Composite Rule into (cos x - sin x) e ^ cos x + sin x (Is this correct?)
I also need to find the particular solution of the differential equation for which y = 1 when x = 0 and then give this particular solution in explicit form..
Many thanks for any help!
If this is , as danny arigo suggests, then it is separable. so . Because, as you say, the derivative of is , that's easy to integrate.
Integrating the equation in "separated" form above gives a "constant of integration". Use that fact that f(0)= 1 to determine that constant.(giving the solution in implicent form)
I have differentiate the function f(x) = e^cos x + sin x using the Composite Rule into (cos x - sin x) e ^ cos x + sin x (Is this correct?)
I also need to find the particular solution of the differential equation for which y = 1 when x = 0 and then give this particular solution in explicit form..
Many thanks for any help!