Solve: (2t)ds + s(2+s^2t)dt = 0
tds + sdt + (1/2)s^(2)tdt
by inspection int factor is 1/st
[d(st)]/st + (1/2)sdt
integrate
ln|st| + 4s^2
Is this right at all?
$\displaystyle (2t)ds + s(2+s^2t)dt = 0$ () just mean multiply and if your multiplying you can rearrange everything your multiplying.
$\displaystyle 2dts + dts(2+s^2t) = 0$ then you can subtract from one side and add it to the other
$\displaystyle dts(2+s^2t) = 0 - 2dts$
$\displaystyle dts(2+s^2t) = - 2dts$ then divide to cancel
$\displaystyle \frac {dts(2+s^2t)}{dts} = \frac{- 2dts}{dts}$
$\displaystyle 2+s^2t = - 2$ then subtract again
$\displaystyle s^2t = - 2 - 2$
$\displaystyle s^2t = - 4$ then divide again
$\displaystyle s^2 = \frac {- 4}{t}$ or $\displaystyle t = \frac {- 4}{s^2}$ depending on what your solving for.
Not trying to be mean but for future note it would be best to post the question just as its asked. Then clearly under it say ... this is what i think: and show your attempt to solve hope this helps
Thanks for the help and you are right I should have said something like "this is my attempt".
One other thing. I am not familiar with this method of solving diff equations. This problem is supposed to be solved by the use of an integrating factor. Since it is not exact and since the form (Mpartial t - Npartial s)/N and (Mpartial t - Npartial s)/-M do not give functions of either t or s alone then I must use inspection.
I am sorry if I am not making sense because it is only my third week in this class, but is my method of inspection correct? Could someone possibly please help me with the correct method of inspection?
Thanks.
hmm ok let me take another look at it real quick.. and try it by inspection.
$\displaystyle (2t)ds + s(2+s^2t)dt = 0$
$\displaystyle (2t)ds + 2sdt+ds^3t^2 = 0$
$\displaystyle s^3t^2d + 2std + s(2t)d= 0$
Sorry i'm not sure on inspection factoring..