
Ordinary equations help
It happens that I'm not good with integrals, and our teacher is a good teacher, but has a little problem: he uses easy examples but gives us difficult homework... I've managed to do most of it, but have trouble with last ones... can anyone help me please? I'm desperate (Crying)!!!
ISolve the next lineal equations:
4.
http://img228.imageshack.us/img228/7734/001on8.gif
II Find the general solution for the next exact ordinary equations:
http://img228.imageshack.us/img228/9266/002wn7.gif
(I know the first one of these is not exact... but can it be solved with an integrating factor?... and the last one... I know it says general solution too... do you think is a trap from my teacher [last time he said "one of the problems didn't have any solution", so I get that wrong...])
Also... procedures will be highly appreciated n__n"
And, after the answers... can someone teach me the art of EDO?... I'll be very grateful, thanks in advance.

$\displaystyle
\begin{gathered}
\frac{{dP}}
{{dt}} + 2tP = P + 4t  2 \hfill \\
\Leftrightarrow \frac{{dP}}
{{dt}} + (2t  1)P = 4t  2 \hfill \\
\Leftrightarrow e^{t^2  t} \frac{{dP}}
{{dt}} + e^{t^2  t} (2t  1)P = e^{t^2  t} \left( {4t  2} \right) \hfill \\
\end{gathered}
$
$\displaystyle
\begin{gathered}
\Leftrightarrow \frac{d}
{{dt}}\left( {e^{t^2  t} P} \right) = e^{t^2  t} \left( {4t  2} \right) \hfill \\
\Leftrightarrow e^{t^2  t} P = \int {e^{t^2  t} \left( {4t  2} \right)dt = 2} \int {\left( {2t  1} \right)e^{t^2  t} dt = 2} e^{t^2  t} + C \hfill \\
\Leftrightarrow P(t) = 2 + Ce^{t  t^2 } \hfill \\
\end{gathered}
$
Exact FirstOrder Ordinary Differential Equation  from Wolfram MathWorld

Thank you~!!! I had it almost done (via general formula, tough), but the integration ruined me u.u... thanks again ^^!