What did I do wrong in solving this basic differential equation?

[Tzabcan]

I have this basic differential equation du/dt=(u^2)*(sin t)

This is obviously a separable diff eq.

So what I've done is:

g(t) = sin t h(u) = u^2

1/(u^2) du = sin t dt

Integrating both side...

1/y = - cos t + c

therefor y = - 1/(cos t + c)Which is wrong, there isn't supposed to be a minus sign apparently. I don't know what I've done wrong. Any suggestions? Thanks.

 

[pasmith]

I have this basic differential equation du/dt=(u^2)*(sin t)

This is obviously a separable diff eq.

So what I've done is:

g(t) = sin t h(u) = u^2

1/(u^2) du = sin t dt

Integrating both side...

1/y = - cos t + c

$\frac{d}{du}(u^{-1}) = - u^{-2}$, so you should have $$-\frac1u = -\cos t + c$$

therefor y = - 1/(cos t + c)Which is wrong, there isn't supposed to be a minus sign apparently. I don't know what I've done wrong. Any suggestions? Thanks.

 

[Tzabcan]

$\frac{d}{du}(u^{-1}) = - u^{-2}$, so you should have $$-\frac1u = -\cos t + c$$

Ah! Wow I'm so dumb haha, 3 hours sleep :D lol.

Thanks a lot.