please help with entire question 7(0) = -5. Consider the initial value problem 47" + 28y'...
Consider the initial value problem 3u" - u'+ 2u = 0, u(0) = 5, u'(0) = 0. (a) Find the solution u(t) of this problem. u(t) = _______ (b) For t > 0, find the first time at which |u(t)|=10. (A computer algebra system is recommended. Round your answer to four decimat places.)t = _______
Consider the initial value problem (a) Find the solution u(t) of this problem. u(t) = b) For t > O find the first time at which lu t = 10 A computer algebra system is recommended. Round your answer to four decimal places.) 回Show My Work (optional:@
Please help me with the
following thermo question from the picture and below
continuation
(b) Based on an inspection of the direction field, describe how
solutions behave for large t.
All solutions seem to eventually have negative slopes, and hence
decrease without bound.All solutions seem to eventually have
positive slopes, and hence increase without
bound. The solutions appear to be
oscillatory.If y(0) > 0, solutions appear to eventually
have positive slopes, and hence increase without bound. If
y(0) ≤ 0,...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
Consider the following. (A computer algebra system is recommended.) 11y' − 2y = e−πt/2, y(0) = a (b) Solve the initial value problem. y(t) = Find the critical value a0 exactly. a0 = (c) Describe the behavior of the solution corresponding to the initial value a0. For a0, the solution is y(t) =
Question 9: Find the solution of the following initial- value problem, d x x² + xt subject to the initial condition dt 12 X = 1 at t = 1
1. For the initial value problem y' = 3y2/3, y(2) = 0, there is a trivial solution, y(x) = 0. Find a nontrivial solution to this IVP. Does this contradict the existence theory for solutions of first onder IVPs y = f(x, y), y(x) = yo? Briefly explain. (VALUE: 4 l ations:
5. Try again < Previous You have answered 0 out of 2 parts correctly. Consider the initival value problem: y' – 0.24 +0.01y = 0, y(0) = 14, 7(0) = b. a. Find the solution in terms of b. Give your answer as y=... . Use x as the independent variable. Answer: y=belx + 146.lx b. Determine the critical value of b that separates solutions that grow positively from those that eventually grow negatively. critical value of b =
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(2 points) Consider the initial value problem -,[0 1 y 1 0 -4 2(O) a. Form the complementary solution to the homogeneous equation. b. Construct a particular solution by assuming the orm УР t = a + t and solving or he undetermined constant vectors a and c Form the general solution (t) c(t)(t) and impose the initial condition to obtain the solution of the initial value problem. n(t) y2(t)
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...