Write the order of the differential equation whose solution is y = a cos x + b sin x + c e–x.
Solution of differential equation is
y = a cos x + b sin x + c e–x ---(1)
Since it has 3 constants a, b, c we differentiate it by 3 times
Differentiate w.r.t x we get,
---(2)
Again, differentiate w.r.t x we get,
---(3)
Again, differentiate w.r.t x we get,
---(4)
Equation (3) implies
From (1)
---(5)
Now, adding equation (2) and (4) we get,
is the required differential equation.
Here the order of differential equation is 3.