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Mod note: HTML size = ... tags are not needed. You can make things look just fine using [ tex ] tags instead of [ itex ] tags.

So, I was doing some stuff, messing around when I thought of something. What if I took a random physics formula and integrated it into the original function? Then I was like, whoa! Is this a differential equation? I worked it like this... [tex]\Delta y = V_i + \frac{1}{2}gt^{2}[/tex]

So that is my formula, now I shall make it be equal to the derivative of velocity with respect to time using the form of dy/dx[tex]\frac{dv}{dt}= V_i + \frac{1}{2}gt^{2}[/tex]

Then I multiply dt to the other side.[tex]dv = (V_i + \frac{1}{2}gt^{2}) dt[/tex]

Then I integrated both sides.[tex]\int dv = \int (V_i + \frac{1}{2}gt^{2}) dt[/tex]

And I obtained...[tex] v = \frac{1}{2}V_i^{2} + \frac{1}{2}(\frac{1}{3}gt^{3}) + C [/tex]

Once I differentiated back, I got the original vertical motion formula! Is this a differential equation? If so, what kind?

So, I was doing some stuff, messing around when I thought of something. What if I took a random physics formula and integrated it into the original function? Then I was like, whoa! Is this a differential equation? I worked it like this... [tex]\Delta y = V_i + \frac{1}{2}gt^{2}[/tex]

So that is my formula, now I shall make it be equal to the derivative of velocity with respect to time using the form of dy/dx[tex]\frac{dv}{dt}= V_i + \frac{1}{2}gt^{2}[/tex]

Then I multiply dt to the other side.[tex]dv = (V_i + \frac{1}{2}gt^{2}) dt[/tex]

Then I integrated both sides.[tex]\int dv = \int (V_i + \frac{1}{2}gt^{2}) dt[/tex]

And I obtained...[tex] v = \frac{1}{2}V_i^{2} + \frac{1}{2}(\frac{1}{3}gt^{3}) + C [/tex]

Once I differentiated back, I got the original vertical motion formula! Is this a differential equation? If so, what kind?

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