Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0)=1, x₂ (0) = 4, and x3 (0) = 6.x' =- 22-26-220 24- 20 - 202 x; x₁ = e2-2t6-551x₂ = ²t - 11The particular solution is x₁ (t) = x₂(t)=, and x3 (t) = .1- 10

System of linear differential equations Advance maths

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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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Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0) = 3, x₂ (0) = 1, and x3 (0) = 5. 3 X' = 10 14 2 x; x₁ = e -2₁ X₂ = ²t GHHM 2 -13 -17 -2 -10-10 2 The particular solution is x₁ (t) = x₂(t)=, and x₂ (t) = . X3 0 c
1.3.1 Use elementary operations to solve the system of equations 3x + y = 3 x + 2y = 1.
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.
Write the given system in the form x' = P(t)x+ f(t). x' = 3x-7y+z+t y' = x-5z+t²2² z' = 3y - 5z+t³ ---
Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0) = 2, x₂ (0) = 3, and x3 (0) = 7. X' = - 27 - 28 2 25 26 - 25 - 25 - 2t - 2 x; x₁ = e 3 The particular solution is x₁ (t) = 6 -5 5 X₂ (t) = X₂ =e³t| nd x3 (t) = and 1 1 X3 1
Find a solution, (x,y), of the following system of two nonlinear equations for which both x and y are real and strictly positive. g(x,y) = 4*x^2 + 5*x*y - 2 = 0 %3D h(x,y) = 9*y^2 + 3*x*y - 3 = 0 Such a solution exists. Report ONLY the x value. You must report your answer so that |your answer - correct answer| < 0.0001 to receive full marks. Do not use scientific notation when reporting your solution.
Find a particular solution of the indicated linear system that satisfies the initial conditions x, (0) = 3, X2 (0) = 4, and x3 (0) = 8. - 18 - 22 - 2 1 1 - 2t 2t x' = 2 x; X1 = e - 4 X2 = - 1 4t X3 = e - 1 16 20 - 16 - 16 2 4 1 ... The particular solution is x, (t) =, xX2(t) =, . and x3(t) =
Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0) = 5, x₂ (0) = 5, and x3 (0) = 8. 3 [1-4-1-4 3t x' = 12 16 1 x; x₁ =e -2, X₂= 2 - 15 - 19 - 12 - 12 3 The particular solution is x₁ (t) = X₂ (t) = and x3 (t): = 4t x3 = e 0
B1. Account
Find the general solution of the given system. - (¹⁰ X(t) = X'= Need Help? 8-12, Read It

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Find a particular solution of the indicated linear system that satisfies the initial conditions x₁ (0)=1, x₂ (0) = 4, and x3 (0) = 6. x' = -22-26-2 20 24 - 20 - 20 2 x; x₁ = e 2 -2t 6 -5 5 1 x₂ = ²t - 1 1 The particular solution is x₁ (t) = x₂(t)=, and x3 (t) = . 1 - 1 0