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

Options

A. 5
B. 6
C. 3
D. 2

Answer

c

Explanation

` y (c_(1) +c_(2)) cos (x+c_(3))=c_(4e^(x+c_(5))`
` y = (c_(1) +c_(2)) cos (x+c_(3))-c_(4)e^(C_(5))*e^(x)`
` rArr y = A cos (x+c_(3))- Be^(x)`
where ` A= c_(1) + c_(2) and B = c_(4)e^(5)`
It has three arbitrary constant so, the order of differential equation is 3.