My method gives you a second order differential equation for x. Solve for x!
[imath]\dfrac{d^2x}{dt^2} = 2 \dfrac{dx}{dt} + 3 \left ( 2\left[\frac{\dfrac{d^2x}{dt^2} - 2 \dfrac{dx}{dt} - 3y}{6}\right] + \dfrac{1}{3} \left ( \dfrac{dx}{dt} - 2\left[\frac{\dfrac{d^2x}{dt^2} - 2 \dfrac{dx}{dt} - 3y}{6}\right] \right )\right)[/imath]
[imath]\dfrac{d^2x}{dt^2} = 2 \dfrac{dx}{dt} + 3 \left ( \frac{2}{6}\dfrac{d^2x}{dt^2} - \frac{4}{6}\dfrac{dx}{dt} - \frac{6}{6}y + \dfrac{1}{3} \left ( \dfrac{dx}{dt} - \frac{2}{6}\dfrac{d^2x}{dt^2} - \frac{4}{6}\dfrac{dx}{dt} - \frac{6}{6}y \right )\right)[/imath]
[imath]\dfrac{d^2x}{dt^2} = 2 \dfrac{dx}{dt} + 3 \left ( \frac{2}{6}\dfrac{d^2x}{dt^2} - \frac{4}{6}\dfrac{dx}{dt} - \frac{6}{6}y + \frac{1}{3} \dfrac{dx}{dt} - \frac{2}{18}\dfrac{d^2x}{dt^2} - \frac{4}{18}\dfrac{dx}{dt} - \frac{6}{18}y \right)[/imath]
[imath]\dfrac{d^2x}{dt^2} = 2 \dfrac{dx}{dt} + \frac{6}{6}\dfrac{d^2x}{dt^2} - \frac{12}{6}\dfrac{dx}{dt} - \frac{18}{6}y + \frac{3}{3} \dfrac{dx}{dt} - \frac{6}{18}\dfrac{d^2x}{dt^2} - \frac{12}{18}\dfrac{dx}{dt} - \frac{18}{18}y [/imath]
The differential equation still has y.
Elimination, as in the algebraic case, will not work here.
I am sure 100% elimination must work.
I want you to show me any competent Differential Equations student who does NOT know that the d in dx is not a variable. Otherwise, do you believe that dx/dt = x/t??
Me. I am a super competent differential equation student. This is the first time I know dx is not a multiplication.
You have to find the second order differential equation for x(t) and solve it to find x(t).
I tried but I think that there must be something wrong in your method. My suggestion is to solve in Matrix style. If this is your method of solving linear system, I suppose you don't have an idea about solving the same system with Matrix, don't you? The Matrix is a straightforward method, but the characteristic equation is annoying somehow.
Your qualifications show themselves in your abilities. This is not as hard a problem as solving the Airy equation.
Yeah I beat the Airy equation. Don't worry, that was nothing comparing to the difficult things I have encountered.
If you really have or are taking a class in Partial Differential Equations, this really isn't all that hard. So please shut up about the Airy equation and buckle down and take your lumps for making a stupid mistake.
Why should I shut up about the Airy equation if I have taken a class in partial differential equation? This Airy is very necessary, so Steven or you must not under grade my skills. Any time you or others shrink my high level math, the Airy equation will pop up again to prove the reverse. By the way, I solved it from scratch!
Now, where in my three step programme are you getting lost?
I am not lost. I am just saying I don't understand it fully as I am sure 100% it must be missing something that is letting it not working properly.
Please, look at my steps and let me know if I was missing something.
You mistakenly said that I am wrong. I never said that you should solve for dy/dt or dx/dt. YOU solved for dy/dt--just look at post 1.
No Steven G, at post 1 I solved for x and I tried to solve for y. Not dy/dt.