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How does MATLAB Simulink get such accurate ODE solution results?

I have a fixed-step model (0.001s) in Simulink in which a second order ODE is effectively being set up, a free spring-mass-damper system (m=2, c=0.3, k=1, x0=0, x_dot_0=4). I am studying the solvers ...
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Is it allowed to use the quadratic solution formula for a differential equation

I have some trouble with a challenging fluid mechanics problem. The problem leads me to a non-linear ode 1st order. $0={\dot p_C}^2+\frac{k_1}{k_2 C}\dot p_C+\frac{p_C-p_0}{k_2C^2}$ My Idea was now ...
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Reciprocal -block in Simulink?

I have nonlinear-differential -system for water-flow. I need to find the reciprocal -block in Simulink. I could do it with reciprocal-sqrt -block and sum -block but too complicated, there must be some ...