6. Consider the intial value problem: 494"' + 42y + 9y = 0, y(0) = a...
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 =
You have answered 0 out of 2 parts correctly. Consider the intial value problem: 644" + 80y + 25y = 0, y(0) = a < 0, y(0) = 5. a. Find the solution in terms of a. Give your answer as y=... . Use x as the independent variable. Answer: _ 5x 8 8 y=cle +62xe b. Find the critical value of a that separate solutions that become positive from those that are always negative. critical value of a =
4. X Try again < Previous Next > Your answer is incorrect. Solve the intial value problem: 4y" – 12y' + 9y = 0, y(-2) = -2, y(2) = 3. Give your answer as y=... . Use t as the independent variable. 3t 2-3 Answer: 1 y= 3(1+2) +e®(31–8))
ITEMS SUMMARY < Previous Next Solve the intial value problem: 25y" – 30y' +9y = 0, y(-1) = 2, y'(1) = -4. Give your answer as y=... . Use t as the independent variable. Answer: Submit answer Answers Answer Score -13 Instructions 0/13 Type here to search
(1 point) Consider the following initial value problem: y" +9y (st, o<t<8 y(0) = 0, '(0) = 0 132, ?> 8 Using Y for the Laplace transform of y(t), i.e., Y = C{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(8)
Solve y'' +9y = $(t – 6), y(0) = y'(0) = 0 g(t) = for t < 6 for t > 6
(1 point) Find the function yn oft which is the solution of 494" – 9y = 0 y(0) = 1, 41(0) = 0. with initial conditions Yi = Find the function y of t which is the solution of 49y" – 9y = 0 with initial conditions Y2 = y2(0) = 0, $(0) = 1. Find the Wronskian W(t) = W(41, 42). (Hint: write y, and y2 in terms of hyperbolic sine and cosine and use properties of the hyperbolic...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
(1 point) Consider the following initial value problem: 4t, 0<t<8 \0, y" 9y y(0)= 0, y/(0) 0 t> 8 Using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where xo + 0, b) no solution exists if y (0) = yo # 0, and c) an infinite number of solutions exist if y (0) = 0.