The general solution of the system of coupled equations =2+ay, bx+cy can be written asD[(t)]= C₁[3]e + Ca[2]Determine the values of aand cGive the values of Cand C₂ =(as a decimal) if a(0) = 1, y(0) = -2.

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Answered: D The general solution of the system of…

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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The break-even point occurs where the graphs of C and R intersect. Thus, we find this point by solving the system (x) = 500,000 + 400x |R(x) = 600x [y = 500,000 + 400x or ly = 600x. Using the substitution method, we can substitute 600x for y in the first equation. 600x = 500,000 + 400x Substitute 600x for y in y= 500,000 + 400x. 200x 500,000 Subtract 400x from both sides. x = 2500 Divide both sides by 200. Back-substituting 2500 for x in either of the system's equations (or functions), we obtain R(2500) = 600(2500) = 1,500,000. We used R[x) = 60ox.
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Use EROS and backward substitution to solve the system Ax= b, where (三) (6) 21 1 and 1. -3 -1 What is the rank of A?
The concentrations of glucose and insulin in an individual interact with each other and vary over time. A mathematical model for the concentrations of insulin and glucose in an individual is given by the system x = x1 + 3 x2 x2 = 4 x1 + 5 x2 Find the general solution for this system. Then find the formula for = 2 and x2(0) x1(t) and x2 (t) if x1 (0) = 1.
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2х — 4y = -34, 1x — 2у = -17. - (a) How many solutions does the system have? If infinitely many, enter "Infinity". Infinity (b) What are the solution to the system? If there are no solutions, write "No Solution" or "None" for each answer. If there are infinitely many solutions let y = t and solve for x in terms of t. X = -17+2t y =
Find the general solutions of the system. - 13 -9 x' = 1 -7 1 3 - 10
Solve the following system 3 y1 = -yı = -Y1 – 5Y3 233 3/2 1 Y2 +,43 2y3 = (a) yı = cie- + 2c3e2 (b) yı = ce¯* – C3e2 (c) y1 = cie* = cje¯* + 2c3e² (b) y1 = c1e- Y2 = c2e" + cze2* Cze?¤ (c) y1 = c1e¯ 2x Y2 = cze" + c3e2* Cze? C2eª Cze2r 92 = Y3 = 2c3e2 -2x = cje Y3 = 2c3e2" -2x Сзе (е) у1 — Сје Y3 = 2c3e2" (d) ул + 2cze" - -2x Y2 = C2e + C3e“ -2x Y2 = C2e + C3e 2x Y3 2c3e Y3 = 2c3e -2x
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Find the General Solution of the system Y' AY (-3 2 3. = 2-3 2 2 =1, 2, = 2, =-5 1. 3. 2.

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D The general solution of the system of coupled equations =2a+ay, be + cy can be written as 3 [8] = a[1] e + Ca [2] Determine the values of a and c Give the values of C and C₂ = (as a decimal) if (0) = 1, y(0) = -2.