Consider the initial value problem 1 i, (0) = 0 -5 Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use t as the independent variable in your answers. a (t) = c1 + c2 help (formulas) help (matrices) Solve the original initial value problem. x1 (t) = help (formulas) x2(t) : help (formulas)

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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.