Q. 55.0( 2 Votes )

Show that the function y = A cos2x – B sin 2x is a solution of the differential equation

Answer :

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

y = A cos2x – B sin 2x, now we find the value of .

= –2A sin 2x – 2B cos 2x

= –4A cos 2x + 4B sin 2x

Putting the values in the equation, we get,

–4A cos 2x + 4B sin 2x + 4(A cos 2x – B sin 2x) = 0,

0 = 0

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

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