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.