I have the differential equation:

dx/dt=x^{2}+5x-6

I have to find the equilibria and solve them.

Second I have to answer the question:

Let x_{1}(t) be its particular solution such that x_{1}(t_{1})=-7 - for some time instant t1. Is it possible that x_{1}(t)=2 for some t? Explain.

To be honest, I have no clue about how to answer to the second question...

I find the points by setting:

0=x^{2}+5x-6

x=-6 or x=1

to get the equilibrium points:

df/dx=2x+5

= 17 for x=-6 and 7 for x=1

so both points are unstable.

Is this true? - How can I answer the second question.

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Another quick question:

Is the differential equation linear? Is it separable?

x'=x^{2}+e^{t}+e^{x}

No it's not linear because it contains the second power of x. It's not separable, because it can not be written as dx/h(x)=t*g(t)

Is this the right answer?