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## Homework Statement

xg=x*(dv/dt)+v^2 is a differential equation

Which has a solution of the form v=at

Where a is a constant.Find a

## Homework Equations

dv/dt=v*(dv/dx)

V=dx/dt

A=dv/dt=d^2x/dt^2

## The Attempt at a Solution

I assumed 'a' as a function of g

That is a=kg for some constant k

And proceeded

I did get the correct answer a=g/3

My question is since both a and g are accelerations and constants

Is it correct to assume one as a function of the other?

For 2 arbitrary constants a and b, we have (a=kb) for another constant 'k' where a and b are never equal to zero at the same time

I hope my approach is correct

Any confirmations and insights are much appreciated!

UchihaClan13[/B]