2 Solving the Basic Factors From Problem s in Project 1, you know that if you have a factorizatio...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
I Do We Have the Complete Solution Set? A differential operator in R[D] has order n can be written out in the form o(n-1) with the last coefficient cn (at least) not equal to zero. The key to determining the dimension of these solution spaces is the following existence and uniqueness theorem for initial value problems. 'So it can be efficiently described by giving a basis. ethciently described by giving a basis Theorem 1 (Existence and Unique ness Theorem for...
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(1 point) Use the Laplace transform to solve the following initial value problem: x' = 5x + 3y, y = -2x +36 x(0) = 0, y0) = 0 Let X(s) = L{x(t)}, and Ys) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for YS) and X (s): X(S) = Y(s) = Find the partial fraction decomposition of X(s) and...
Have som problem solving this problems in MATHEMATICAL METHODS
2.
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Problem 1. Solve the following systems of linear equations: 4x+3y + z = 9 3x+y-z = 3 x4 Problem 2. Find the values of the parameters a and p for which the system x+5y = 6, has: (i) a unique solution, (ii) infinitely many solutions, (iii) no solutions. Hint: Use the following fact: a system with as many unknowns as equations...
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Problem #1 From ECE 102 Engineering Computation textbook-, problem #1, page 126: Note: C is coulombs of charge, A is amperes of current The flow of charge in a conductor varies with time according to the function g(t)=(1-3,-)C a) Ifk -0.1s, find the current atl e Express your result rounded to 3 decimal places dt b) What is the current for very large values of time r?...
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Problem 1 (weight 25%) Consider the problem Maximise f(x, y, z) = x + y +2z when g(x,y,z) = x2 +y2 +2z2 = 4. (*) (a) Explain why the problem (*) does have a solution (b) Suppose that ( has a solution, and use Lagrange's method to set up the necessary conditions for solving the problem. (c)Find all the triplets (r. y, 2) that satisfy the necessary conditions for solving the problem (*),...
(1 point) We consider the non-homogeneous problem y" + 4y = -32(3x + 1) First we consider the homogeneous problem y" + 4y = 0: 1) the auxiliary equation is ar? + br +c= r^2+4r = 0. 2) The roots of the auxiliary equation are 0,4 (enter answers as a comma separated list). (enter answers as a comma separated list). Using these we obtain the the complementary 3) A fundamental set of solutions is 1,e^(-4x) solution yc = cyı +...
help solving the unique solution of the IVP
W *) As a specific example we consider the non-homogeneous problem y" - 16y = 482** (1) The general solution of the homogeneous problem (called the complementary solution, y Independent solutions, y. y. Here a and bare arbitrary constants. d y + by is given in terms of a pair of linearly Find a fundamental set for y' - Toy = 0 and enter your results as a comma separated list 6^(4x),0^-(4x)...
Homework #6-Due Monday, March 11th Problem 1. Solve the IVP Problem 2. Solve the IVP Prolem 3. Solve the IVP Problem 4. Show that the set e-isto-rfundamestal wt f o Problem 5.Isa).ga)sina)) afulamestal set of solutiono with 0 x?Explain Problem 6. Consider the ODE and sappose that the oots for the characteristk equation+c0 ae the pair of Show that einco(Bt)is a fundamentall set of olutions for this ODE HINT: You will need the fact that given a quadratic ﹃watin ar'...
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HW3: Problem 7 Previous Problem Problem List Next Problem (1 point) Fundamental Existence Theorem for Linear Differential Equations Given the IVP dz1 d"y d" - 4.(2) +4-1(2) +...+41 () dy +40()y=g(2) dr y(t) = yo, y(t)= y yn-1 (3.) = Yn1 If the coefficients (1),..., Go() and the right hand side of the equation g(1) are continuous on an interval I and if (1) #0 on I then the IVP has a unique solution for...