#1
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Elementary diff Eq question
I took all my math too fast and I went and forgot it all.
Anyways I'm reviewing differential eq's and I need to solve x''(t) + 9x'(t) + 14x(t) = -28 Where x'(0)= 0, x(0)=10. Now I remember how to do this for the form ax''(t) + bx'(t) + cx(t) = 0 I know it has something to do with the characteristic polynomial and a general form but its all fuzzy in my head. |
#2
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Re: Elementary diff Eq question
Solve for the homogeneous equation:
rē+9r+14=0 (r+7)(r+2)=0 x1=C1exp(-7t) x2=C2exp(-2t) Solve for the inhomogeneous sol'n: x(t)=x1+x2+X The inhomogeneous part is of the form of a constant, so set X=A where A is a constant. X'=X''=0 --> Plug into original diff eq 0+9*0+14*A=-28 A=-2 Therefore: x(t)=C1exp(-7t)+C2exp(-2t)-2 Take first derivative, plug in BCs, and you get: x(t)=(84/5)exp(-2t)-(24/5)exp(-7t)-2 |
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