Answer Happy

[20] 3. DiffEq [2] a. Indicate which of the following statements are correct (+) or incorrect (-) A differential equation describes the relationship between a function, its derivatives and the variable on which they depend. The explicit form of a DE expresses a function as a linear combination of its derivatives An ordinary DE consists of only linear functions The order of an ODE refers to the highest derivative of the function in the equation. [4] b. Solve the following initial value problem y + 2y = 4 y(0) = 10 [5] c. Use the method of Variation of the Constant to solve the following 1st order ODE 2xy' + y = 2√x [7] d. Find the general solution of the following 2nd order ODE y" + 15y' + 56y = e-6x [2] e. The equation mx + Bx +kx = 8(t-to) describes the ringing of a bell, where 8(t - to) is the so-called "Dirac delta function" (zero for all t except t = to, where it is equal to 1), which represents the near instantaneous single strike of the hammer on the bell at time to. What is the domain of the coefficient B if the bell's ring slowly trails off with time after to? 1.2 T 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -2 -1 Dirac delta function 0 1 2