5 Solution of the differential equation $y'' + 2xy' + \left( 1 + x^2 \right)y = 0$ via power series 3 Show that $\displaystyle\left(\sum_{r=1}^n r\right)^2=\sum_{r=1}^n r^3$ without expanding to closed form 2 Equation of conic: Given five points on it 1 Finding exact value of infinite series. 1 Show that series is convergent and find its sum

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 5 How to prove that this diophantine equation has only two solutions? 4 How to solve this particular difference equations? 3 Find two arithmetic progressions of three square numbers 3 How to prove that this limit is zero? 3 Closed form of the elliptic integral $\int_0^{2\pi} \sqrt{1+\cos^2(x)}\,dx$

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 5 ordinary-differential-equations × 4 2 determinant 5 power-series 2 conic-sections 3 summation × 2 1 sequences-and-series × 7 2 coordinate-systems 1 calculus × 6 2 analytic-geometry 1 trigonometric-series

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