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In Problems 21–24, solve the given initial value problem using the method of Laplace transforms. Sketch the graph of the solution.
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Chapter 7 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- QUESTION 2 If the auxiliary equation of a certain linear, homogeneous, 8th order DE with constant coefficients factors to. (m+3)(m +2m+5) =0 O y(x) =(4+4x)e" cos(2x) + (B, +B,x)e" sin(2x) +(C, +C,x+C)* y(x)=(4+4,x)e"cos(3x) + (B, +B,x)e" sin(3x) +(C+Cx+C,)* O y(x) =(4+4x)e cos(2x)+(B, +B,x)e" sin(2x)+(C+Cx)e" O y(x) =(4+4,x)cos(2x) +(B, + B,x) sin(2x) +(C+C,x+Cx)* -3r QUESTION 3arrow_forwardProblem 6.5 Find the Hamilton-Jacobi-Bellman equation for the sys- tem *1(t) = x2(t) i2 (t) = -2.x2(t) – 3x7(t)+ u(t) with the performance index as J = [" (-11) + u°(1) dt. stf 2arrow_forward1. Linearize the following equations: (a) f(x) = x¹/3 + cos(x) around xo = π/2. (b) g(x) = -3x³ + sin(4x2) around xo = 2.arrow_forward
- QUESTION 17 Provide an appropriate response. Find y' for y = y(x) defined implicitly by 3xy - x² - 4-0. O 2x-3y O V ******** 3x |3y - 2x 3x 3x-2v 4 y = 3xarrow_forwardProblem 2 (Exercise 2.4.6) Find the general solution. x" – 2x' +x =0arrow_forwardProblem 7.4: Find the PS of (x' = 4x - 3y y' = 3x + 4y x(0) = 2 y(0) = 1arrow_forward
- 4. Calculate the Complex Fourier coefficient c, for the periodic function m-narrow_forwardProblem 7.7: Use LT to find the PS of x"" +x" + x + x = et (x(0) = x'(0) = x" (0) = 0arrow_forwardProblem 4.2 (Textbook: Figure 2.5 on P84): Hypothetically, a patient is diagnosed to have P, coronavirus at time t = 0 and these viruses grow subsequently (nobody really knows the truth but we assume) according to = -aP(M – P) where P(t) is the number of the cells at time t while a and M are two given positive constants. The patient will die when the number of bugs approaches infinity. Consider the case Po > M, find the time the patient has left to live, timed from t = 0. Your result is a formula with the given parameters Pg, M, a. For a more concrete example, please set P, = 1984, M = 1000, a = 1. Compute the patient's survival time. Never mind if the number is small when you use , a = 1 as no unit is given. If you insist having a "reasonable" number, I set a = 10* for which the time unit is week. Either number you use is correct for your HW solution.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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