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## Homework Statement

Given [itex]\dot{x} \equiv { \mathrm{d}x \over \mathrm{d}t }[/itex] and [itex]\ddot{x}[/itex] is [itex]{ \mathrm{d^2}x \over \mathrm{d}t^2 }[/itex]

what is solution for x(t) and y(t) which satsifies

[itex]2 \ddot{x} y + 3 \dot{x} \dot{y} + x \ddot{y} = 0[/itex]

## Homework Equations

[itex]2 \ddot{x} y + 3 \dot{x} \dot{y} + x \ddot{y} = 0[/itex]

## The Attempt at a Solution

clearly, guesses could be made for x(t) and y(t) but is there a most general solution which somehow includes all possible solutions?

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