In Problems 11–16 verify that the
13.
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FIRST COURSE IN DIFF.EQ.-WEBASSIGN
- Tr.28.arrow_forwardProblem 2. Consider the equation: x?y"(x) – xy' +y = 0. Given that yı(x) = x is a solution of this equation. Use the method of reduction of order, find the second solution y2(x) of the equation so that y1 and y2 are linearly independent. (Hint: y2(x) should be given in the form y2(x) = u(x)y1(x). Substitute it into the equation to find u(x).) %3Darrow_forward11.3 11.4: Problem 7 Find the linearization L(x, y, z) of the f(x, y, z) = 2/ x³ + y³ + z³ at the point (1, 2, 3). Answer: L(x, Y, z) =||arrow_forward
- The same disease is spreading through two populations, say Pi and P2, with the same size. You may assume that the spread of the disease is well described by the SIR model. dSa - BaSaIa dt dla - dt dRa YaIa dt with Sa(0) + I.(0) + R.(0) = N where N denotes the fixed population size. The subscript a identifies the population P or P2. For example, if a = 1, the variables are related to P1. Assume that S1 (0) = S2 (0) and I1(0) = I½(0) and that no interventions such as quarantine or vaccination have been implemented. If the difference in the spread of the disease is due only to the poor over-all health of a population, which population has the best over-all health of the two populations? - Susceptible Population 1 - Susceptible Population 2 700 600 500 400 300 200 100 10 15 20 t P1. P2. Susceptiblearrow_forward10. Find the general solution of the system of differential equations 3 -2 -2 d. X = -3 -2 -6 X dt 3 10 1 + 2tet + 3t?et + 4t°et 3 1 -3 Hint: The characteristic polymomial of the coefficient matrix is -(A- 4)²(A- 3). Moreover (:) 2 1 Xp(t) = t²et +t³et +t'e3t -1 -1 -3 is a particular solution of the system.arrow_forward.The system x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7)x′=3(x+y−13x3−k),y′=−13(x+0.8y−0.7) is a special case of the Fitzhugh–Nagumo16 equations, which model the transmission of neural impulses along an axon. The parameter k is the external stimulus. a.Show that the system has one critical point regardless of the value of k.arrow_forward
- 8.1 I only need number 22 pleasearrow_forward8. Solve the given (matrix) linear system: X' = ; *+(*) (3cos(t) 14 2 2etarrow_forward1. Verify that the formulas for Bo and B1 for linear equation ŷ = Bo + B1x from A = (X" X)-1 X" Y are the same as those formulas that we mentioned before. That is ( is short for Σ) nEriy; – (Ex;)(E4%) B1 Ex? – nữ? n Bo = – B1ữ XiYi (E4i)(E) – (Dr;)ET:y; nE – (E#)²arrow_forward
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