Find the differential equation whose general solution is given by `y=(c_(1)+c_(2))cos(x+c_(3))-c_(4)e^(x+c_(5))`, where `c_(1),c_(2), c_(3), c_(4), c_(5)` are arbitary constants.

Options

A. 5
B. 4
C. 2
D. 3

Answer

D

Explanation

We have,
`y=(C_(1)+C_(2))sin(x+C_(2))-C_(4)e^(x+C_(5))`
`rArr" "y=C_(6)sin(x+C_(3))-C_(4)e^(C_(5)).e^(x)," where "C_(6)=C_(1)+C_(2)`
`rArr" "C_(6)sin(x+C_(3))-C_(7)e^(x)," where "C_(4)e^(C_(5))=C_(7)`
Clearly, the above relation contains three arbitrary constants. So, the order of the differential equation satisfying it is 3.