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Differential Equations and Linear Algebra (4th Edition)
- Find the general solution of the given system dx/dt = -4x +2y dy/dt = -5/2x+2yarrow_forwardFind the general solution of the given system. dx/dt=3x-y dy/dt=9x-3yarrow_forwardfirst write the given system of differential equations in matrix form, and then determine all solutions. Q. x′ 1 =3x1−4x2−x3, x′ 2 =− x2−x3, x′ 3 =− 4x2+2x3.arrow_forward
- You are given the following inhomogeneous system of first-order differentialequations for x(t) and y(t) in matrix form: x ̇ = 2x + y + 3 et ,y ̇ = 4x − y Write down the general solution of the original inhomogeneous systemarrow_forward1. If y = (x + 1/x) (2x-3, then dy/dx will be ? 2. If matrix A is (2 5) (3 4) and f (x) = x2 +4 , what is the answer to f (A)?arrow_forwardFind the general solution of the given system. dx dt = 7x + 5y dy dt = −2x + 9yarrow_forward
- Consider the following. x1' = 3x1 − 2x2, x1(0) = 3 x2' = 2x1 − 2x2, x2(0) = 1 2 (a) Transform the given system into a single equation of second order by solving the first equation for x2 and substitute into the second equation, thereby obtaining a second order equation for x1.' (b) Find x1 and x2 that also satisfy the initial conditions.arrow_forwardApply the Gauss-Seidel method to the systemarrow_forwardHow much longer should you expect Gaussian elimination to work on a system of 1000 equations versus a system of 500 equations?arrow_forward
- 1. for the case of repeated real roots what would the general solution be?2. if i was to let y1(t) = theta(t) as well as y2(t) = theta'(t)=y1'(t) how could i show that the initial equation could be written as a system of 1st order odes that involved y1 and y2. the system will then need to be presented as a the matrix equation y' = Myarrow_forwardFind the general solutions of the system. x′= 1 0 −4 −1 3 −1 1 0 5 x x(t)=enter your response herearrow_forwardYou are given the following system of differential equations: dx/dy = 6x + 2y, dy/dt = 2x + 9y You are told that the coefficient matrix is: [6 2] [2 9] and this matrix has eigenvectors: [1] and [-2][2] [1] and the corresponding eigenvalues of 10 and 5. What is the general solution of this system?arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning