7. The general solution of a non homogeneous state-space equation is given below. Use the initialconditions to determine the value of C₁.[] = ² [2¹] + ₂² [2] + [1C₁e2₁given x(0) = 0, x'(0) = 2You calculated that C₁ = 913+914 jNote that if C₁ is a real number that 914 = 0.

The general solution to a nonhomogenous state-space equation given is as follows:…

Answered: 7. The general solution of a non…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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6. A population is modeled by the function P(t): 500 where t represents time in years. 2+3e-t Determine a) The initial population according to the model. b) The time in years until the population reaches 200.
Are the functions f,g,f,g, and hh given below linearly independent? f(x)=0, g(x)=cos(8x), h(x)=sin(8x) If they are independent, enter all zeroes. If they are not linearly independent, find a nontrivial solution to the equation below. Be sure you can justify your answer.
Use the method of undetermined coefficients to determine the form of a particular solution for the given equation. y'"' + 10y" – 11y=xe* + 4x What is the form of the particular solution with undetermined coefficients? Yp(x) = ] (Do not use d, D, e, E, i, or I as arbitrary constants since these letters already have defined meanings.)
Suppose 2 = f(). (a) Given y(xo) = = Yo, when does this equation have a unique solution? (b) Make a substitution z = how to separate the variables. z(x, y) to transform this equation into a separable one. Show (c) Construct an example of such an equation and solve it using the substitution found in (b).
2. Which of the following is a general solution to the following: x²y" + xy' + (36x² - 1) y (Hint: As discussed in the lecture, use Y, only when J, and J-, are linearly dependent). A. y = c₁J₁(2x) + C₂J_1(2x) 6 B. y = C₁J₁(x) + C₂Y₁(x) 3 3 C. y = c₁₂/₁(6x) + C₂Y₁(6x) 0 D. y = c₁J₁(6x) + c₂] _1(6x) 2
Verify that the functions y= + Find the solution of the IVP ry' +y=x², y(3) = 2. are a one-parameter family of solutions of the DE ry' +y = x2. Also, determine the value of C and state the actual solution. Type the LHS and RHS that verified your answer in simplest form. Note, for example, if your answer is 2x3a y = %3D 5 type it in the form y = frac{2x^{3a}}{5} . %3D
3. Find the general solution, given ₁ satisfies the complementary equation. As a byproduct, find a fundamental set of solutions of the complementary equation (2x+1)y"-2y'-(2x+3)y=(2x+1); y₁ = ex

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7. The general solution of a non homogeneous state-space equation is given below. Use the initial conditions to determine the value of C₁. [*]=G₁²) [2¹] + C₂e\ +C₂e(-2) 1 + [4] given x(0)=0, x'(0) = 2 You calculated that C₁ = 913+914 j Note that if C₁ is a real number that 914 = 0.