Arbitrary Constant

Question

using elimination of arbitrary constant, determine differential equations satisfied by the following functions: x=c1e^6t + c2te^6t

a. x" - 36x' + 12x = 0

b. x" + 12x' - 36x = 0

c. x" - 12x' + 36x = 0

d. x" - 4x' + 9x = 0

Answer 1

x' = 6c₁e^6t + c₂e^6t + 6tc₂e^6t; x'' = 36c₁e^6t + 12c₂e^6t + 36tc₂e^6t;

x'' - 6x' = 6tc₂e^6t_;

x' - 6x = c₂e^6t; x'' - 36x = 12c₂e^6t; (x' - 6x)/(x'' - 36x) = 1/12; x'' - 36x = 12x' - 72x; x'' - 12x' + 36x = 0

Answer is c.