Use Variation of Parameters to find the general solution of the equation Py" (t) – 4ty (t) + 6y(t) = t³ + 1, t>0 The Variation of Parameters guarantees a particular solution in the form Yp(t) = y1 (t)v1 (t) + y2(t)v>(t). Hint: The functions y1 (t) = t° and y2(t) = t³ are linearly independent solutions of the homogeneous solution for t > 0. (a) The Wronskian of y1(t) and y2(t) is W (y1, 42)(t) : (b) Find the function v1(t) vi(t) =

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A: The detailed solution is as follows below:

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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.