Use the properties of a Cauchy-Euler system to find a general solution of the given system....
Use the properties of a Cauchy-Euler system to find a general solution of the given system. 8 5 tx' (t) = X(t), t> 0 - 8 21 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t) = t'u if and only if ris an eigenvalue of A and u is a corresponding eigenvector. X(t) = 0
Use the properties of a Cauchy-Euler system to find a general solution of the given system. 2 9 tx'(t) X(t), t> 0 -2 13 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t) = t’u if and only if ris an eigenvalue of A and u is a corresponding eigenvector. x(t) =
Use the properties of a Cauchy-Euler system to find a general solution of the given system. 3 7 tx'(t)= X(t), t> - 3 13 For t>0, any Cauchy-Euler system of the form tx' = Ax with A an nxn constant matrix has nontrivial solutions of the form x(t)= t'u if and only ifr is an eigenvalue of A and u is a corresponding eigenvector. x(t) = 0
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
A9.5.36 Question Help Find a general solution to the system below. -2 x(t) x'(t) = This system has a repeated eigenvalue and one linearly independent eigenvector. To find a general solution, first obtain a nontrivial solution x, (t). Then, to obtain a second linearly independent solution, try x2 (t) = te"u, + e"u2, where r is the eigenvalue of the matrix and u, is a corresponding eigenvector. Use the equation (A - rl)u, = u, to find the vector u,....
Find a general solution to the given Cauchy-Euler equation for t> 0. 12 2d²ydy + 40 - 10y = 0 dt dt The general solution is y(t) = 0
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)
Find a general solution to the given Cauchy-Euler equation for t> 0 fy"(t) - 9ty' (t) + 25y(t) = 0 The general solution is yt) = D.
Find the general solution to the following non-homogeneous Cauchy-Euler equation. Use the method of variation of parameters to find a particular solution to the equation *?y" - 2xy' + 2y = x?, x>0.
Find a general solution to the given Cauchy-Euler equation for t> 0. 2d²y dy +41 - 10y = 0 dt at² The general solution is y(t) =