5. Write the following higher-order differential equations as equivalent systems of (first order) differential equations: (a) r" – 21" + 5x' + 10x = t³e# + 2x" + 5(x")3 +t*rr' + cos(x) = 1+ t2 Do NOT write these in matrix-vector form. (b) x"

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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.