Q. 16

# Write the order of the differential equation associated with the primitive y = C1 + C2 ex + C3 e–2x + C4, where C1, C2, C3, C4 are arbitrary constants.

y = C1 + C2 ex + C3 e–2x + C4 ---(1)

Since it has 4 arbitrary constants C1, C2, C3, C4 we differentiate it by 4 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)

Again, differentiate w.r.t x we get,

---(5)

Now, (2) – (3) we get

---(6)

Now, (4) – (5) we get

From (6)

is the required differential equation

Here the order of differential equation is 4.

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