Differential equations time evolution

[Katy96]

Homework Statement

Homework Equations

The Attempt at a Solution

Any help would be appreciated

 

[SteamKing]

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.

 

[Katy96]

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.

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

 

[TomW17]

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

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.

 

[HallsofIvy]

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".

 

[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.