i know nothing about differential equations cause ive only done calc 2 but my brother and i were thinking about a physics problem and we came up with this differential equations (where x and y are both funtions of a parameter t)

btw: i coulnt figure out how to type leibniz notation so when i write x' or y' i mean with respect to t.

y'' = y/[4(x^2+y^2)^3]

x'' = x/[4(x^2+y^2)^3]

how can I get a graph of this curve (on the xy plane) given:

-an interval for the parameter t
-initial conditions for x' and y'
-initial conditions for x and y

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Origionally I had it in vector form

P(t)=integral(Vi)dt + 0.25*integral integral [P(t)/(magnitude of P(t))^3] dt dt

where P(t) is the position vector, and Vi is the initial Volocity.
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really all i want is a graph of the curve. Is there a program or anything that can help me do this?