Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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4
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1answer
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Behaviour of solutions to ODE near singular points

I am having trouble understand how to classify what happens to solutions of ODE near singular points. For example, I have a question that is about the ODE; $$(x^2-36)y''+(6-x)y'+(x^2+12x+36)y=0$$ ...
2
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1answer
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Legendre Differential Equation, $y_1,y_2$ linearly independent solutions

$$(1-x^2)y''-2xy'+p(p+1)y=0, p \in \mathbb{R} \text{ constant } \\ -1 < x<1$$ At the interval $(-1,1)$ the above differential equation can be written equivalently $$y''+p(x)y'+q(x)y=0, ...