I have a question on DE but its really the graph that puzzles me.

[Sonal7]

How would i have known that the graph would look like this. Yes I could just choose lots of values and plot the graph. I think that the method here? Just checking.

 

[Deleted member 4993]

Did you solve the DE? What is the solution?

In the graph:

which variable is plotted on the horizontal axis?

which variable is plotted on the vertical axis?

 

[HallsofIvy]

From \(\displaystyle \frac{dx}{dt}= \frac{8}{x}\), we can immediately get \(\displaystyle xdx= 8dt\). What do you get when you integrate both sides of that? Do you understand that \(\displaystyle \int xdx=\frac{1}{2}x^2+ C\)? Do you know what the graph of a quadratic looks like?

 

[Sonal7]

Yes I integrated this to x squared =16t-7
I guessed it's a quadratic. I plotted x along x axis. It does make sense the graph should look like this.

 

[HallsofIvy]

Why does it not make sense? You know that the graph of a quadratic, y= ax^2, is a parabola, do you not? Here, since x is a function of t and it is t that is squared, the axis of symmetry is along the x-axis. You would probably have recognized it if you had chosen the horizontal axis to be t, the independent variable, and the vertical axis to be x, the dependent variable.