Thread: seperation of variables help

do i take the ln or do i use partial fractions i dont know how t start it plz help

Originally Posted by bsanghera

do i take the ln or do i use partial fractions i dont know how t start it plz help

Separate

$\displaystyle
\frac{dy}{\sqrt{1-y^2}} = \frac{dt}{t}.
$

[quote=Danny;381710]Separate

$\displaystyle
\frac{dy}{\sqrt{1-y^2}} = \frac{dt}{t}.
$[/quote

lol yess i kniw that much but i was asking what to do aftr that do i take the natural log?

[quote=bsanghera;381729]

Originally Posted by Danny

Separate

$\displaystyle
\frac{dy}{\sqrt{1-y^2}} = \frac{dt}{t}.
$[/quote

lol yess i kniw that much but i was asking what to do aftr that do i take the natural log?

So $\displaystyle \sin ^{-1} y = \ln t + c = \ln t + \frac{\pi}{2}$ (from the IC).

Taking sin's gives

$\displaystyle
y = \sin \left(\ln t + \frac{\pi}{2}\right)
$.