The value of the constant 'm' and 'c' for which y = mx + c is a solution of the differential equation `D^2y` - 3Dy -4y = -4x is:

Options

A. is `m= - 1 , c= 3//4`
B. is `m= 1 , c= -3//4`
C. no such real m,c
D. is` m = 1, c= 3//4`

Answer

3

Explanation

`y, mx+c,(dy)/(dx)=m,(d^(2)y)/(dx^(2))=0`
`"subsitituting in" (d^(2)y)/(dx^(2)) -3 (dy)/(dx)-4y=-4x`
`0-3x-4(mx+c)=-4x`
-3m-4c-4mx=-4x`
`-(3x+4c)=4x(m-1)`
(i) "true for all real" x if
`n=+1 "and" c =- 3//4`