3. (a) Find the eigenvalues and eigenfunctions of the boundary-value problem x2y'' + xy' + (lamda)y = 0,  y(1) = 0,  y(5) = 0 (b) Put the differential equation in self-adjoint form. (c) Give an orthogonality relation.

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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.