title: Solving ODEs with SymPy
body: <p>I've just started trying out SymPy. Unfortunately, I am already stumped. Behold this:</p>
  <pre><code>from sympy import *
  t, G, M = symbols('t G M', real = True)
  x = Function('x')
  y = Function('y')
  print(Eq(Derivative(x, t, 2),  G * M * x(t) / (x(t) * x(t) + y(t) * y(t))**1.5))
  </code></pre>
  <p>...it simply prints <code>False</code>. The <a href="https://docs.sympy.org/latest/modules/core.html#sympy.core.relational.Equality" rel="nofollow noreferrer">documentation</a> says that this means the relationship can be <em>proven</em> to be false.
  I know that I can prevent evaluation by using <code>evaluation = False</code>, but eventually I want to solve my system of differential equations, and then this assumption will come into play again.</p>
  <p>So, can anyone see what I did wrong here?</p>
  <p><strong>Addendum:</strong></p>
  <p>What I am trying to do is play around with the two-body-problem and orbital mechanics. With the gravitational constant <code>G</code> and the mass of the primary <code>M</code> at the origin, this and the symmetric equation for <code>y(t)</code> describe the gravitational acceleration on the secondary.</p>
  <p>The solution, Kepler tells us, should be an ellipse for reasonable starting conditions.</p>