Using Python, Consider the following nonlinear initial value problem, du 2 dt = tu+2u with the initial condition u(0) = -5,0≤t≤5, and step size, h = 0. Using the implicit Euler method by deriving the recursion formula and by using Newton's method. Plot both solutions and along with the analytical result u(t) = -20e 2t 2t 9-5e +10te 2t
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- N.png ... If gcd(a, m) = 1, then the unique solution xo to ax = b (mod m) is equal to (1) xo = ab (mod m) (2) xo = ab (mod m), where b is the inverse of b. (3) xo = ām (mod m), where ā is the inverse of a. (4) xo = āb (mod m), where ā is the inverse of a. A Choice (2) (B) Choice (1) Choice (4) (D) Choice (3)solve using PYTHON/matlabPlease do the following question with the required python coding. Question is in the photo.
- Simplify the following Boolean function F, together with the don’t-care conditions d, and then express the simplified function in sum-of-minterms form: F(A,B,C,D)= ∑(2,4,10,12,14) d(A,B,C,D)= ∑(0,1,5,8)Please do the following questions with the full python coding and explanation below each question typedPYTHON/JUPYTER NOTEBOOKS Program a backward solver (i.e. write your code) for an upper triangular system Ux=b. The algorithm is attached for i and j with offset 1. Recall that NumPy and Python have offset 0 for their sequence data types.
- Please help with an explanation. All running times refer to the worst-case analysis.An oscillating current in an electric circuit is described by i(t) = 9e cos(2rt) where t is in seconds. Use False Position Method to determine the value of t such that i=3.5. Plot the graph of the function to develop your initial guess. Terminate your computation when the approximate relative error falls below ɛs=10°. Give the results in a table.Prove, by finding constants C₁, C₂, and no that satisfy the definition of order of magnitude, that f= (g) if f(x) = log(3x²) and g(x) = log x. Note, you will need some of the log rules.
- Please help step by step with an explanation for Program R (CS) with a final code for understanding thank you.I have been confused for a while on worst case, best case, and average case for algorithms. I get that big O noation is worst case, Omega notation is best case, and theta is average notation, but I don't get how are we supposed to be able to tell what the function (ex. (n), (log n), ( n log n), etc.) is for those algorithms and why are they those functions?Using the Definitional proof, show that each of these functions is O(r²). (a) f(r)= 5x (b) f(r) = 5x +5 (c) f(x)= 5x² + 5x + 5 (d) f(x)= 5x² + 5log(x) %3D