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hope this helps
1) The complete table is shown in the attachment .
2) The direction field is shown in attachment.
3) The given differential equation is:

We separate variable to get:

We integrate both sides wrt x to get:

This implies that:


Or

We apply the initial condition:



The particular solution is:

4) See attachment
Black absorbs light, which makes it the "hottest" colour. White reflects light making it cooler, so your answer would be white
Hope this helped :)
Elements emit colours when heated because electrons in atoms can have only certain allowed energies.Heating an atom excites its electrons and they jump to higher energy levels. When the electrons return to lower energy levels, they emit energy in the form of light. Every element has a different number of electrons and a different set of energy levels. Thus, each element emits its own set of colours. See, for example, mercury and neon above. Those colours are as distinctive to each element as fingerprints are to people.