solve X′ = AX by providing two linearly independent solutions of the form v(t). In each case identify the equilibrium at (0,0) as either a nodal source, nodal sink, saddle point, spiral source, spiral sink, center or non-standard. X' = AX where A = [-2  4 ]                                           [0    2]   *this is a 2x2 matrix

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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.