Differential Equations

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13 Terms

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∫1/(x²+1)dx

arctan(x)+C

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∫1/(x²-1)^.5dx

arcsin(x)+C

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∫1/(x²+1)^.5dx

arccos(x)+C

4
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Equation for Heat Loss

T’=k(T-TA)

5
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Spring Equation

mx’’+cx’+kx=F(t)

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critically damped

c²-4mk=0 1 root with multiplicity 2

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overdamped

c²-4mk>0 (2 real roots and has no oscilitation)

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underdamped

c²-4mk<0 (imaginary roots and has oscilation)

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Amplitude

C=(A²+B²)^.5

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Phase Shift

B/A=tan(gamma)

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Angular Frequency

w=(k/m)^.5

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Solution for spring problems

x=Acos(wt)+Bsin(xt)=Ccos(wt-gamma)

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Circuits Solution

LI’’+RI’+I/C=E’(t)