Consider Legendre equation (1-x²)y"-2xy'+ n(n+1)y=0 Write this equation in Sturm-Liuville form and identify the weight function for orthogonality. Show that the first few integrals of the solutions with respect co the weight function are orthogonal. Po(x)=1 P1(x)=x P2(x)=(1/2)(3x² -1) P3(x)=(1/2)(5x³-3x)

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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.