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.