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True or False Ivp questions a) An IVP of the for y' + p(t)y = g(t),...
Theorem 2.1 Consider an IVP of the form y' + g (x)ya h(x), y(%)-yo. Assume that g(x) and h(x) are both continuous on some interval a < x < b and that a < xo < b. Then there exists a unique solution y(x) to the initial value problem that is defined on a <x<b Theorem 2.2 Consider an IVP of the form y' = f (x.y), y(xo) = yo. Assume that ftxy) andfx, y) are both continuous on a...
For each initial value problem, does Picards's theorem apply? If so, determine if it guarantees that a solutio exists and is unique. Theorem (Picard). Consider the initial value problem dy = f(t,y), dt (IVP) y(to) = Yo- (a) Existence: If f(t,y) is continuous in an open rectangle R = {(t,y) |a<t < b, c < y < d} and (to, Yo) belongs in R, then there exist h > 0 and a solution y = y(t) of (IVP) defined in...
Question 10 Incorrect Mark 0.00 out of 4.00 p Flag question Given the IVP y(0) = 1 Without explicitly solving the ODE, indicate which of the following statements are true. Select one or more: a. The existence and uniqueness theorem guarantees the existence of a unique solution defined in an interval (h, h). b. The existence and uniqueness theorem guarantees the existence of a unique solution defined in an interval (1 - h. 1 + h). X c. The solution...
I need some help with these true false questions for linear algebra: a. If Ais a 4 x 3 matrix with rank 3, then the equation Ax = 0 has a unique solution. T or F? b. If a linear map f: R^n goes to R^n has nullity 0, then it is onto. T or F? c. If V = span{v1, v2, v3,} is a 3-dimensional vector space, then {v1, v2, v3} is a basis for V. T or F?...
Problem 5. Given vi,v2,... ,Vm R", let RRm be defined by f(x)-x, v1), x, v2), (x, Vm where (x' y) is the standard inner product of Rn Which of the following statement is incorrect? 1. Taking the standard bases Un on R": codomain: MatUn→Un(f)-(v1 2. Taking the standard bases Un on R: codomain: v2 vm) Matf)- 3. f is a linear transformation. 4. Kerf- x E Rn : Vx = 0 , where: Problem 8. Which of the following statements...
[7] 1. Consider the initial value problem (IVP) y′(t) = −y(t), y(0) = 1 The solution to this IVP is y(t) = e−t [1] i) Implement Euler’s method and generate an approximate solution of this IVP over the interval [0,2], using stepsize h = 0.1. (The Google sheet posted on LEARN is set up to carry out precisely this task.) Report the resulting approximation of the value y(2). [1] ii) Repeat part (ii), but use stepsize h = 0.05. Describe...
pls do all questions. thanx 1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...
5. Let y E C2([0, T]; R), T > 0 satisfy y"(t) = 피t, y(0) = y'(0) = 0 e R. Use Picard-Lindelöf 1+t' to prove that a unique solution to the IVP exists for short time, as follows: (a) Let b E R2, A E M2 (R) . Show that any function g : R2 -R2.9(x) = Ax+b is Lipschitz. 1 mark (b) Transform the DE for y into a(t) Az(t) +b(t) for a suitable z, A, b. 2...
Consider the following IVP y″ + 5y′ + y = f (t), y(0) = 3, y′(0) = 0, where f (t) = { 8 0 ≤ t ≤ 2π cos(7t) t > 2π (a) Find the Laplace transform F(s) = ℒ { f (t)} of f (t). (b) Find the Laplace transform Y(s) = ℒ {y(t)} of the solution y(t) of the above IVP. Consider the following IVP y" + 5y' + y = f(t), y(0) = 3, y'(0) =...
need help with #3 L. (3Upts) Consider the following ivp I)(24), 2(0) = 1.5. ut show that this ivp has a unique solution that exists everywhere on (-00, oo). Sk etch the graph of this solution with explanations (monotonicity, concavity,..) ow that the following initial value problem has a unique solution that exists for all t. cos(a) cos(et), a" +sin(a") cos(a') i r(0)-1, r"(0) = 0 . 4. (30 pts) Consider the following ivp r, y, 2x + y +...