# first order differential equation from variational calculus problem has me stumped!

• Sep 30th 2010, 04:41 AM
punkstart
first order differential equation from variational calculus problem has me stumped!
This arises when solving the problem of Dido,

$\frac{\dot x}{\sqrt{1+\dot x^2}} = -\frac{t}{\lambda} + C$, where C and $\lambda$ constant

They mention that it can be solved by direct integration or by using the substitution $\dot x =tan(\alpha)$.

The solution is given as circles of the form $(\frac{t}{\lambda}-d)^2+(\frac{t}{\lambda}-k)^2 = 1$ where d and k are constants of integration.

I don't know how to deal with that many differentials of x on the same side of the equation! I need some guidance here !
• Sep 30th 2010, 06:21 AM
Ackbeet
Well, what do you get on the LHS when you do the indicated substitution?
• Oct 1st 2010, 06:18 AM
punkstart
i get sin ? Let me work on it a little more, thanx for the tip !
• Oct 1st 2010, 06:20 AM
Ackbeet
Sounds good so far. Keep going!
• Oct 3rd 2010, 05:54 AM
gaurav5
First of all substitute z for (C - t/λ) on the R.H.S. and don't forget to change from dx/dt
to dx/dz on the L.H.S. Then solve for dx/dz , to get it as a function of z.Now integrate both sides using tables....