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Second order homogenous differential equation

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Show that y=t and y=1/t are solutions of

t^2*y" + ty' - y = 0

Determine the following solutions of this equation, or explain why none exist.

y(1)=0, y'(1)=2

all solutions satisfying y(t)=0 as t approaches zero

all solutions satisfying y(t)=0 as t approaches infinity.

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