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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.