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.α=2 β=2 1. Consider the following initial-value problem. y' = e(1+B)* In(1 + y²), 0<t<1 y...
Alpha=9 beta=3 yazarsin 1. Consider the following initial-value problem. y' = e(1+B)t ln(1 + y2), 0<t<1 y (0) = a +1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t = 0.5. {"
1. Consider the following initial-value problem. s y' = e(1+B)t In(1 + y2), 0<t<1 y (0) = a +1 a) b) t=0.5. Determine the existence and uniqueness of the solution. Use Euler's method with h = 0.25 to approximate the solution at
x=6 1. Consider the following initial-value problem. Sy' = e(1+B)t In(1 + y2), 05t51 y (0) = a +1 {" 3:2 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t = 0.5.
alpha = 3 beta =2 Can you solve it in a hour please Thank you very much. 1. Consider the following initial-value problem. y' = e(1+B)t ln(1 + y2), 0<t<1 y (0) = a +1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) (15p.) Use Euler's method with h = 0.25 to approximate the solution at t=0.5. {
B=1 1. Consider the following initial value problem. V = n(1 + y²), OSI31 y(0) = 0+1 a) ( 15p.) Determine the existence and uniqueness of the solution. b) ( 15p.) Use Euler's method with h = 0.25 to approximate the solution at t=0.5. 2=8
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...
Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t 1. For a tolerance of e-0.01, use a based on absolute error stopping procedure Consider the initial value problem given below dx -2 +t sin (x), dt x(0) 0 Use the improved Euler's method with tolerance to approximate the solution to this initial value problem at t...
Consider the initial value problem x^2 dy/dx = y - xy, y(-1) = 1 Use the Existence and Uniqueness theorem to determine if solutions will exist and be unique. Then solve the initial value problem to obtain an analytic solution.
6. (2 pts) Consider the following initial value problem: y' = (t + y)?y2 + sin(yº) + yety, y(0) = 0. This initial value problem satisfies the existence and uniqueness theorem criteria using interval (-0, 0) for both thet and y variables, and hence has a unique solutoin. Find this unique solution. Hint: None of the techniques we've learned for explicitly solving will work. Instead, try plugging the initial condition into the differential equation and think about what that tells...
Exercise 1 Consider the initial-value problem y(t)=1+3940), 25t<3; y(2) = 0. a) Show that the problem has a unique solution. b) Compute (by hand) an approximation of y(3) using the forward Euler method with a step size h = 0.5 (namely perform 2 steps of the method).