4. Consider the homogeneous linear equation: 2x²y" + 3xy' – y = 0, x > 0. (a) Explain why y = e" is not a suitable guess for a solution to the differential equation. (b) Find the values of r for which y = x" is a solution to the differential equation. (c) Let y1, Y2 be the solutions corresponding to your r-values. Compute the Wronskian and verify that W +0 for x > 0. (d) Identify the general solution.

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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.