Answer :

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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