hw11: Problem 1 Previous Problem Problem List Next Problem (1' point) For the functions f(t) = et and g(t) = e , defined on 0 0. a. Use convolution and Laplace transforms to find the Laplace transform of the solution. Y (s) = [ ty(t) } = b. Obtain the solution y(t). y (t) = 5+16+12 Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 0%. You have unlimited attempts remaining. O HOW Desktop acer F4 F6 F7 8 19 F10 11 F12 PrtSc/Imprecr. Pause Scr LK Arretdef SysRq/Syst. Break/Interr # % A 5 6 8 9 0 = 3 1/4 3/4 R O Ahw11: Problem 3 Previous Problem Problem List Next Problem (1 point) In an integro-differential equation, the unknown dependent variable y appears within an integral, and its derivative dy/dt also appears. Consider the following initial value problem, defined for t 2 0: at 4 1 . alt - whe to do - 8 , " ( 0 ) = 0 . a. Use convolution and Laplace transforms to find the Laplace transform of the solution. Y(s) = Cty(t) } b. Obtain the solution y(t) y(t) Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. O Desktop 18 0 0 0 acer F8 F10 F11 12GOT LK rtSc/Imprecr. Pause Insert Delete/Supp F3 Arretdef SysRq/Syst. Break/Interr. F4 0 # 0 1/4 1/2 3/4 4 C O 6 8 2 9 3 U O P F R A G H K D B N Mhw11: Problem 4 Previous Problem Problem List Next Problem Solutions to linear differential equations can be written using convolutions as y yIVP ( h(t) * f(t ) ) . yivp is the solution to the associated homogeneous differential equation with the given initial values (ignore the forcing function, keep initial values). . h(t) is the impulse response (ignore the initial values and forcing function). . f(t) is the forcing function. (ignore the initial values and differential equation). Use the form above to write the solution to the differential equation y" 9y - 9t2 3t with y(0) - 5, y'(0) - -3 + * If you don't get this in 1 tries, you can get a hint. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers to search Desktop 18 . C acer 6 F7 F8 9 10 11 PrtSc/Imprecr. Ins 3 F4 12 GET L Pause Arretdef SysRq/Syst. Break/Interr. $ 0% & K 0 5 6 8 3 1/4 1/2 3/4 W 4 O P m R Y V G H K