DE test 2
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13 Terms
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dT/dt\=
k(T-Tm)
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dA/dt\=
Rin - Rout
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dP/dt\=
kP(t)
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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
2. term before y'' \=/ 0
3. if x \= x0 is in the interval
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Homogeneous
L(y) \= 0
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nonhomogeneous
L(y) \= g(x)
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linearly dependent
there exist constants c1, c2, ..., not all zero such that c1y1 + c2y2 \=0
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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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linearly independent
the wronskian \=/ 0
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P(x)\=
a1/a2
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u(x)\=
∫(e^-∫P(x)dx)/(y1^2) dx
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y2\=
u(x)y1(x)
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complex number
y\= e^Ax * (c1cosBx + c2sinBx)