Trouble solving an ODE and plotting its phase portrait

[zeesyk]

Mentor note: Moved from non-homework forum to here hence no template.

So I was able to solve part 1.A of the first problem by hand, the phase portrait is a sideways parabola. However, I want to also show on this on mathematica. I want to solve the equation first and then plot the phase portrait it but this is what shows on my screen. What am I doing wrong?

 

[dRic2]

1) That is not the correct equation for free-fall

2) You have to write it like this: differential equation == 0. For example, if you had $y'(t) = t$ you should have written $y'(t) - t = 0$.

3) DSolve should give the analytical solution so there is no need to specify the domain ({t, 0, 10}) you can just write t.