(1 point) Find y as a function of tif y" - 16y=0, y(0) = 5, y(1) = 6. s(t) = Remark. The initial conditions involve values at two points
(16 points) Find y as a function of x if y'" + 25y' = 0, y(0) = -7, y' (O) = -15, y" (0) = 100. y(x) =
(1 point) Find y as a function of t if 16y" – 32y + 20y = 0, and y(1) = 9, y' (1) = 4. y =
Find the general solution to the equation below. " y+ 16y = 0 Find the general solution to the equation below. " y+ 16y = 0
Find the impulse response function. y" +8y' + 16y = g(t)
Question 6 (30 points Solve the initial value problem. y"+8y + 16y = 0, y(0) = 1, y'(0) =1 y(t) = 5e-41 + te-4, Question 7 (30 points) Solve the following equation by undetermined coefficients. -67 5 C2e Question 9 (30 points) Solve for the general solution of the differential equation. Question 10 (10 points) Compute using the table of Laplace Transforms. (s-2) (r-2) (s+2 6 (s+2)
(1 point) Find yy as a function of xx ify′′′+64y′=0,y‴+64y′=0,y(0)=−1, y′(0)=−16, y′′(0)=−192.y(0)=−1, y′(0)=−16, y″(0)=−192.y(x)=
having trouble finding y(t) NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3, /(0)-9. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). (s 2Y(s)-3s-9)+16Y(s) help (formulas) 48/s 2 b. Solve your equation for Y(s). C{y(t))=48/(s 2(s2+ 16)...
Consider the intial value problem: 81y" + 72y' + 16y= 0, y(0) = a > 0, y'(0) = -1. a. Find the solution in terms of a. Give your answer as y=... . Use x as the independent variable. Answer: b. Find the critical value of a that separate solutions that become negative from those that are always positive. critical value of a =
Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y = 8, 7(0) = 1, y'(O) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) y = 8 Find a linear differential operator that annihilates the function g(x) = 8. (Use D for the differential operator.) Solve the given initial-value problem. Y(X)...