Show that the function y = A cos x + B sin x is a solution of the differential equation

The differential equation is and the function that is to be proven as solution is

y = A cos x + B sin x, now we need to find the value of .


= –A sin x + B cos x


= –A cos x – B sin x


Putting the values in equation, we get,


–A cos x – B sin x + A cos x + B sin x = 0,


0 = 0


As, L.H.S = R.H.S. the equation is satisfied, hence this function is the solution of the differential equation.


4