How do you solve, dy/dx=(x^2+y^2)/xy?

Substitute y/x = z then separate the variables and integrate.

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Integrate x^2sin(x) between -pi and pi


The infinite series C and S are defined C = a*cos(x) + a^2*cos(2x) + a^3*cos(3x) + ..., and S = a*sin(x) + a^2*sin(2x) + a^3*sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = a*sin(x)/(1 - 2a*cos(x) + a^2), and find C.


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