2. i) Let f(x, y, z, p,q) be a homogeneous function of degree n of X, y and Z . Show that the equations z = px+qy and f(x, y,z, p,q)= 0 are compatible. ii) Find common solution of the equations z = px+ qy and px² -qy = x² + y(x-z).

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A: differential equation

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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.