Number of values of `m in N` for which `y=e^(m x)` is a solution of the differential equation `(d^3y)/(dx^3)-3(d^2y)/(dx^2)-4(dy)/(dx)+12 y=0` (a) 0 (b) 1 (c) 2 (d) More than 2

Options

A. 0
B. 1
C. 2
D. More than 2

Answer

C

Explanation

`y=e^(mx)` satisfies `(d^(3)y)/(dx^(3))-3(d^(2)y)/(dx^(2))-4(dy)/(dx)+12y=0`
Then `e^(mx)(m^(3)-3m^(2)-4m+12)=0`
or `m=+-2,3`
`m in N`
Hence, `m in {2,3}`