Problem 04
$2t \, ds + s(2 + s^2t) \, dt = 0$
Solution 04
$2t \, ds + s(2 + s^2t) \, dt = 0$
$2t \, ds + 2s \, dt + s^3t \, dt = 0$
$(2t \, ds + 2s \, dt) + s^3t \, dt = 0$
$2(t \, ds + s \, dt) + s^3t \, dt = 0$
$2 \, d(st) + s^3t \, dt = 0$
$\dfrac{2 \, d(st)}{s^3t^3} + \dfrac{s^3t \, dt}{s^3t^3} = 0$
$\dfrac{2 \, d(st)}{(st)^3} + \dfrac{dt}{t^2} = 0$
$2 (st)^{-3} \, d(st) + t^{-2} \, dt = 0$
$\displaystyle 2\int (st)^{-3} \, d(st) + \int t^{-2} \, dt = 0$
$-(st)^{-2} - t^{-1} = -c$