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Hint

1

dT/dt=

k(T-Tm)

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2

dA/dt=

Rin - Rout

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3

dP/dt=

kP(t)

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4

unique solution

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

term before y'' =/ 0

if x = x0 is in the interval

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5

Homogeneous

L(y) = 0

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6

nonhomogeneous

L(y) = g(x)

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7

linearly dependent

there exist constants c1, c2, ..., not all zero such that c1y1 + c2y2 =0

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8

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

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9

linearly independent

the wronskian =/ 0

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10

P(x)=

a1/a2

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11

u(x)=

∫(e^-∫P(x)dx)/(y1^2) dx

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12

y2=

u(x)y1(x)

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13

complex number

y= e^Ax * (c1cosBx + c2sinBx)

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