For the system X"(t) = A(t).X(t)+ B(t),X(0) = 0 where 1 e' e' e' A(t) = e e' 0| and B(t) =| e'| Then, the largest interval where te' te' 1-1 te 1+ 2t the system is guaranteed to have a unique solution is a) (-1-) b) (-) c) (-11) d) [-

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A: This is a problem of Differential Geometry.

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A: Finding the eigenvalues and corresponding eigenvectors.

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Q: homogeneous system for its general solution

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Q: If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:

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Q: y" + 6y' + 8y = e-³te5t, y(0) = 0, y'(0) = 0 a. (e³t-1)²e-5t 3 b. (et - 1)³e5t a C. (et - 1)³e-5t 3…

A: The given initial value problem,.We have to find the solution to the IVP.

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Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

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Q: how do I find critical points of the resulting system.  x'=y y'=-9sin(x)

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Q: I' = - R – I +2 (1) (2) R' = I (d) Which term in equations (1) and (2) do you think in an indirect…

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Q: b) The system of nonlinear equations above has a solution near the point (x₁, y₁) = (1,1). Taking…

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Q: Find exactly T (t) and N(t) for x = [Choose the correct answer.] T (0) = T (0) T (0) T (0) = = = (i…

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Q: Solve the non-homogenous system Sa' = -x – y+ 3/2 ly = 2x – 4y Find lim-00 r(t)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.