Q. 15

# 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.

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