Elimination of Arbitrary Constants

Find the differential equation whose solution is given by y = cx+c

• y' = (x+1)

• y = y' (x+1)

• y = y'

• y=y'(x-1)

Find the differential equation whose solution is given by x²+y² = r²

• xdy+ydx = 0

• xy'+y = 0

• x+y = y'

• xdx+ydy = 0

Eliminate the arbitrary constant: y = ax²+bx+c

• y''' = 0

• y'' + y''' = 0

• y' +y'' + y''' = 0

• y' + y'' = 0

Given : y = c₁ e^-x + c₂ e^2x , eliminate the arbitrary constants c₁ and c₂.

• y+y'' = 3c₂e^-x

• y+2y' = 3c₂e^-x

• y' = 6c₂e^2x

• none of the above

Find the differential equation having the solution as

y = a sin(x+b)

• y+y'' = 0

• y' = a cos (x+b)

• y+y'' = a cos (x+b)

• y-y' = 0