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falling object DE
m(dv/dx)=mg-γv
Ly’’+Ry’+Cy=E(t)
2nd order linear
y’’+msiny=g(t)
2nd order nonlinear
y’+p(t)y=g(t)
1st order linear
integrating factor for 1st order linear
eSp(t)dt
M(x)+N(y)y’=0
1st order separable
mixing problem DE
y’=rincin-routcout
compound interest problem DE
ds/dt=rs+k
velocity problem DE
V(dx/dw)=(-gR2)/(R+x)2
Logistic equation
y’=r(1-(y/K))y
how to tell if a DE is exact
My=Nx
exact DE integrating factor
u’=(My-Nx)u/N
newtons cooling problems
dT/dt=-k(T-a)
falling object problems
m(dv/dt)=mg-Yv