Solve the given clairaut equation

[Marcin H]

Homework Statement

Homework Equations

x=-f'(t)
y=f(t)-tf'(t)

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.

 

[LCKurtz]

Homework Statement

View attachment 95671

Homework Equations

x=-f'(t)
y=f(t)-tf'(t)

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.

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.

 

[Marcin H]

Homework Statement

View attachment 95671

Homework Equations

x=-f'(t)
y=f(t)-tf'(t)

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.

ohhhhhhh. I see that now. Thank you!