Math help

[T.Vengeance]

I just started learning differential equations. I had the basics down last semester. But for my own project I need to solve a non-linear differential equation. 

 

http://www.wolframalpha.com/input/?i=-y%28x%29%27%3Dcy%28x%29%5E2%2Bk

 

^From wolfram alpha. What I don't get is what is a₁?

[NicekillBG]

it has a number :0

[T.Vengeance]

it has a number :0

No as in I don't understand the meaning of a1. Where did it come from? Like in integration, the indefinite integral of x is 0.5x^2 + C, where C is the constant of integration. So in differential eq, what does the a₁ mean?

[rustikles]

Alpha is just a placeholder variable for any real number. Look at what happens when I replace "k" with 2.http://www.wolframalpha.com/input/?i=-y%28x%29%27%3Dcy%28x%29%5E2%2B2 

This time you still have a constant of integration "k1" in your answer, rather than it being called "alpha1". 

[T.Vengeance]

Alpha is just a placeholder variable for any real number. Look at what happens when I replace "k" with 2.http://www.wolframalpha.com/input/?i=-y%28x%29%27%3Dcy%28x%29%5E2%2B2 

This time you still have a constant of integration "k1" in your answer, rather than it being called "alpha1". 

OHH I get it thanks! So alpha 1 is just there to tell you that any real number plugged into alpha 1 will make the differential equation true?

[RazerZ]

Do yourself a favor and don't learn from Wolfram Alpha.

[T.Vengeance]

Do yourself a favor and don't learn from Wolfram Alpha.

I'm not learning from it. I'm using it to solve a drag differential equation with the force of friction.

 

         F= Drag + Friction

 

     ma = kmv² + u_kmg 

 

  dv/dt = cv² + k

 

I just need to solve for v.