Question

form the differential equations by eliminating the arbitrary constants of y=Ae^t+Be^2t? plz write all the steps

Answer 1

$y = a \: {e}^{t} + b \: {e}^{2t}$
this is the complementary function of the
characteristic equation
${p}^{2} - 3p + 2 = 0$
having roots 1 and 2

Therefore corresponding differential equation
is

${y}^{11} - 3 {y}^{1} + 2y = 0$