Differential equations time evolution

1. Aug 6, 2015

Katy96

• Member warned about posting with no effort
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
Any help would be appreciated

Last edited by a moderator: Aug 7, 2015
2. Aug 6, 2015

SteamKing

Staff Emeritus
katy96:
Please try to post your HW problems in the correct HW forum.

Questions about differential equations should be posted in the Calculus HW forum.

Thanks.

3. Aug 6, 2015

Katy96

It was given in a physics class as part of mechanics assignment

4. Aug 6, 2015

TomW17

It's still a calculus problem so should be posted in the relevant section.

For your question, essentially you want to eliminate every derivative of $y$ and have a DE which just involves $x$ and its time derivatives. Start by differentiating $\frac{dx}{dt}$ to obtain an equation for $\frac{d^2 x}{dt^2}$ which will leave you with 3 equations. You can use these to eliminate $y$ and its derivatives.

5. Aug 7, 2015

HallsofIvy

Staff Emeritus
If this was given as a homework problem, surely you have been given some instruction in solving such problems. There are, in fact, several ways to solve this problem. We have no idea which method would be appropriate for you without knowing what methods you have learned. Part of the problem tells you to "Combine these to form a second order equation for x(t) and find the general solution for x(t)". Do you know how to do that?

Start by differentiating both sides of the given equation that starts "dx/dt= " with repect to t. The result will have a second order derivative of x(t) and a derivative of y(t). Use the other equation to replace that "dy/dt".

6. Aug 8, 2015

epenguin

Or else you can obviously eliminate y between these two eqs. but then you are left with dy/dt in the result. Differentiating first eq. you get dy/dx in terms of x and derivatives and t only which you can then substitute into the other equation you just got.

Not something which requires you to be 'taught' a 'method' IMHO, just a bit of initiative or at most to be told it's possible.

Last edited: Aug 9, 2015