The order of the differential equation whose general solution is given by y=C1e2

Question

The order of the differential equation whose general solution is given by

y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5})

Options:

A . 5

B . 4

C . 3

D . 2

Answer: Option B
:
B

y = C_{1} e^{2 x + C_{2}} + C_{3} e^{x} + C_{4} s i n (x + C_{5}) = C_{1} . e^{C_{2}} e^{2 x} + C_{3} e^{x} + C_{4} (s i n x c o s C_{5} + c o s x s i n C_{5}) = A e^{2 x} + C_{3} e^{x} + B s i n x + D c o s x

Here,

A = C_{1} e^{C_{2}}, B = C_{4} c o s C_{5}, D = C_{4} s i n C_{5}

(Since equation consists of four arbitrary constants)

∴

order of differential equation = 4.

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