DE test 2

dT/dt\=

k(T-Tm)

dA/dt\=

Rin - Rout

dP/dt\=

kP(t)

unique solution

1. all terms before y'', y', y, etc. are continuous

2. term before y'' =/ 0

3. 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)\=

∫(e^-∫P(x)dx)/(y1^2) dx

y2\=

u(x)y1(x)

complex number

y\= e^Ax * (c1cosBx + c2sinBx)