Reminders

2.1 Pretty direction fields

f[x_,y_]:= x Sin[x y]
StreamPlot[{1,f[x,y]}, {x,-3,3},{y,-3,3}]

2.2 Separable Equations

Just like in Calc an ODE of the form
	dy/dx = g[x]h[y]
is separable.  You get the general solution by separating variables and integrating
	∫1/h[y]dy = ∫g[x]dx+C.

2.3 Linear 1st Order ODE

Standard form
	y'[x]+P[x]y[x]=f[x]
Compute μ[x]=(e^(∫P[x]dx)) and multiply eq by μ and collapse product rule terms and integrate to get general solution
	({{μ[x]y'[x], +, μ[x]P[x]y[x], =, μ[x]f[x]}, {μ[x]y'[x], +, μ'[x]y[x], =, μ[x]f[x]}, { ,  , (μ[x] y[x])', =, μ[x] f[x]}, { ,  , μ[x]y[x], =, ∫μ[x]f[x]dx+C}})
As always if I have an initial condition I plug it into the general solution.

2.4: Exact

The equation  M dx + N dy =0 is exact if ((∂M)/(∂y))=((∂n)/(∂x)) and the solution is f[x,y]=c where 
 M=((∂f)/(∂x)) and N=((∂f)/(∂y)).  
First integrate f=∫((∂f)/(∂x))dx+g[y]=∫M[x,y]dx+g[y] 
then find g'[y] by differentiating 
((∂f)/(∂y))=N=(∂/(∂y))((∂/∂)∫M[x,y]dx )+g'[y]
finally integrate to get g and write down the general solution f[x,y]=c.
As always if you have an IC you plug into the general solution.