Show that y = e x (A cosx + B sinx) is a solution of the differential equation

Question

Philoid · Accepted Answer

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

y = e^x (A cosx + B sinx), we need to find the value of .

= e^x(A cos x + B sin x) + e^x(–A sin x + B cos x)

= e^x(A cos x + B sin x) + e^x(–A sin x + B cos x) + e^x(–A sin x + B cos x) + e^x(–A cos x – B sin x)

= 2e^x(–A sin x + B cos x)

Putting the values in equation,

2e^x(–A sin x + B cos x) – 2e^x(A cos x + B sin x) – 2e^x(–A sin x + B cos x) + 2 e^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.