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 one year ago
Solve the initial problem
\[y_1''=2y_1+y_2+y_1'+y_2'\]\[y_2''=5y_1+2y_2+5y_1'y_2'\]\(y_1(0)=y_2(0)=y_1'(0)=4\), \(y_2'(0)=4\)
 one year ago
Solve the initial problem \[y_1''=2y_1+y_2+y_1'+y_2'\]\[y_2''=5y_1+2y_2+5y_1'y_2'\]\(y_1(0)=y_2(0)=y_1'(0)=4\), \(y_2'(0)=4\)

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RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.0Note that I put this under linear algebra.

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.0I think it has something to do with eigenvalues and eigenvectors

RolyPoly
 one year ago
Best ResponseYou've already chosen the best response.0and diagonalization too

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1let y'1 = u, and y'2 = v, you get 4x4 system.

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1dw:1357743467559:dw

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1dw:1357743488688:dw

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1let that matrix be A, you get X' = AX < this is logistic equation ... I must admit ... to me, this is not a nice question.

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1the solution is \[ X = Se^{\Lambda t}S^{1}X(0)\]

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1dw:1357745773804:dw

sirm3d
 one year ago
Best ResponseYou've already chosen the best response.0how about laplace transform?

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1dw:1357746034677:dwdw:1357746105903:dw

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1dw:1357746162435:dw

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1dw:1357746200518:dwdw:1357746235140:dw

experimentX
 one year ago
Best ResponseYou've already chosen the best response.1so the final solution is dw:1357746290760:dw

vf321
 one year ago
Best ResponseYou've already chosen the best response.0@sirm3d Using the laplace transform is not as pretty as @experimentX 's cleaner linear algebra solution. You're not guaranteed invertible functions in the frequency domain.
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