Consider the system of equations: x'1 = x1 - 3x2 x'2 = 3x1 + 7x2 The system has a repeated eigenvalue of 4, and vec(x1) = e^{4t} x (1, -1) is one solution to the system. Use the given eigenvector to find a second linearly independent solution to the system, vec(x2).

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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.