Complicated maths problem

SoSolid · 23 Jan 2008 at 20:03

How does one solve the following differential equation;

y" + c*y' ^2 = g, where g is the acceleration due to mavity. I know there a few clever people on here when it comes to maths. I am lost as to how to do this and am going out of my mind trying to get the solution. C is an arbitrary constant.

gumbald · 23 Jan 2008 at 20:12

Is this homework too?

SoSolid · 23 Jan 2008 at 20:22

No it's not homework. I am messing around with projectiles trying to add in air resistance.

SpeedFreak · 23 Jan 2008 at 20:31

not really getting your notation too well here. What is y" and y'?

Phyre · 23 Jan 2008 at 20:38

I'm guessing 2nd and 1st derivatives

SpeedFreak · 23 Jan 2008 at 20:42

Phyre said:
I'm guessing 2nd and 1st derivatives

actually just realised that too, thanks.

SpeedFreak · 23 Jan 2008 at 20:47

Looks to me as if this is point of terminal velocity, where resistance is equal to mavity.

SoSolid · 23 Jan 2008 at 20:50

This is an equation describing the acceleration of the particle in the y direction. And yes it is a second order differential equation.

SpeedFreak · 23 Jan 2008 at 20:57

so in essence this can be described as:

a+c*(v^2)=g

gonna have to dig out my Maths for Physical Science book to jog the memory.

SoSolid · 23 Jan 2008 at 21:01

Yes it can mate. I would like to obtain the equation to describe its displacement in the y direction, however. Would be very grateful if you could help me, I am totally lost.

SoSolid · 23 Jan 2008 at 21:37

No one have any ideas?

Coran · 23 Jan 2008 at 21:50

Use a general solution of y=Aexp(Bx)+C.
Find the derivates, put in and solve.

SoSolid · 23 Jan 2008 at 21:52

I have been trying to do that but have totally forgot the technique, I now use laplace transforms to solve differential equations but I cannot use them for this case.

Coran · 23 Jan 2008 at 22:09

Ok so it's either harder or easier than we thought. What's the situation? Can you just put y=Ax+B as a solution? That would come out quite easily I expect simply because y'' would be 0. It does seem like a bit of a cheat and somewhat pointless if that were the case though.