dT/dt=
k(T-Tm)
dA/dt=
Rin - Rout
dP/dt=
kP(t)
unique solution
all terms before y'', y', y, etc. are continuous
term before y'' =/ 0
if x = x0 is in the interval
Homogeneous
L(y) = 0
nonhomogeneous
L(y) = g(x)
linearly dependent
there exist constants c1, c2, ..., not all zero such that c1y1 + c2y2 =0
Wronskian
a mathematical determinant whose first row consists of n functions of x and whose following rows consist of the successive derivatives of these same functions with respect to x
linearly independent
the wronskian =/ 0
P(x)=
a1/a2
u(x)=
ā«(e^-ā«P(x)dx)/(y1^2) dx
y2=
u(x)y1(x)
complex number
y= e^Ax * (c1cosBx + c2sinBx)