Q. 125.0( 1 Vote )

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

Answer :

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

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


= ex(A cos x + B sin x) + ex(–A sin x + B cos x)


= ex(A cos x + B sin x) + ex(–A sin x + B cos x) + ex(–A sin x + B cos x) + ex(–A cos x – B sin x)


= 2ex(–A sin x + B cos x)


Putting the values in equation,


2ex(–A sin x + B cos x) – 2ex(A cos x + B sin x) – 2ex(–A sin x + B cos x) + 2 ex(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.


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