If y = e^ -mx is a solution of the differential equation d^2y dx^2 + 4 dy dx + 3y = 0 , then the values of m are

Step-by-step solution

Given y = e^ -mx Differentiating with respect to x , we get: dy dx = -m e^ -mx d^2y dx^2 = m^2 e^ -mx Substituting these into the given differential equation d^2y dx^2 + 4 dy dx + 3y = 0 : m^2 e^ -mx + 4(-m e^ -mx ) + 3(e^ -mx ) = 0 e^ -mx (m^2 - 4m + 3) = 0 Since e^ -mx 0 for any finite x , we have: m^2 - 4m + 3 = 0 (m - 1)(m - 3) = 0 m = 1, 3 Answer: 1, 3