# Thread: Diff Eq. x' = t * cos(t)²

1. ## Diff Eq. x' = t * cos(t)²

Am I doing this right?

x' = t * cos(t)²
x = t * sin(t)²
And that's it?
Or should I change the "t" variable into: 0.5t², in the t in front of the sin function? As in should I derive a T, if so, which one?

And if it says x(0) = 1, what should I do with it?

2. Originally Posted by ManyTimes
Am I doing this right?

x' = t * cos(t)²
x = t * sin(t)²
And that's it?
Or should I change the "t" variable into: 0.5t², in the t in front of the sin function? As in should I derive a T, if so, which one?

And if it says x(0) = 1, what should I do with it?
please confirm one or the other ...

$x' = t \cdot \cos(t^2)$

or

$x' = t \cdot \cos^2{t}$

?

3. Actually it is written without parenthesis:
x' = t cos t²

So my guess: x' = t cos(t²)

4. Originally Posted by ManyTimes
Actually it is written without parenthesis:
x' = t cos t²

So my guess: x' = t cos(t²)
$dx = t\cos(t^2) \, dt$

substitution ... $u = t^2$ , $du = 2t \, dt$

$x = \frac{\sin(t^2)}{2} + C$