Solve the given clairaut equation

1. Feb 11, 2016

Marcin H

1. The problem statement, all variables and given/known data

2. Relevant equations
x=-f'(t)
y=f(t)-tf'(t)

3. The attempt at a solution
Solution in picture. This is the solution to this problem, but I have no idea where the y^2=4t^6 comes from. Doin this problem I get everything up until y=2t^3 and then using x=3t^2 I solved for t and plugged it in, but that's not working. I did every other clairaut's problem like this, but I have no idea where this one goes after the y=2t^3 step.

2. Feb 11, 2016

LCKurtz

You have $x = 3t^2$ and $y=2t^3$. He is just eliminating the $t$ by noting if you cube the $x$ and sqare the $y$ both equations will have a $t^6$ so you can eliminate it easily.

It would be much easier to follow the thread if you would type the equations instead of posting images, as per forum rules.

3. Feb 11, 2016

Marcin H

ohhhhhhh. I see that now. Thank you!!!!