Find the values(s) of w for which y=cos(wt) satisfies the differential equation. Enter your answers as a comma-separated list.
$$\frac{d^{2}y}{dt^{2}}+4y=0$$

Question

Find the values(s) of w for which y=cos(wt) satisfies the differential equation. Enter your answers as a comma-separated list.
$$\frac{d^{2}y}{dt^{2}}+4y=0$$

wmj259 · Answer

To solve this equation piece by piece. Take the second derivative of y=cos(wt)

wmj259 · Answer

The first derivative, is -wsin(wt). Correct?

kkutie7 · Answer

here let me give you what I have

kkutie7 · Answer

$$y=cos(wt),            y'=-tsin(wt),                 y"=-t^{2}cos(wt)$$
and of course:
$$y"+4y=0$$

wmj259 · Answer

If I am not mistaken you should be taking the derivatives with respect to t's because you should at the end be solving for w.

kkutie7 · Answer

opps you're right here let me rewrite it:
$$y=cos(wt),            y'=-wsin(wt),                 y"=-w^{2}cos(wt)$$
$$y"+4y=0$$

wmj259 · Answer

I apologize, I just got myself into a tongue-twister. 
Let me start again.

The derivatives you should be computing should be with respect to t's by treating w's as a constant.

kkutie7 · Answer

$$like this\rightarrow -w^{2}cos(wt)=+4(cos(wt))$$

kkutie7 · Answer

there shouldn't be an equals sign there that was a typo

kkutie7 · Answer

yup that worked the answer was 2, -2. thanks for the help!