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RolyPoly
 3 years ago
Solve the initial problem
\[y_1''=2y_1+y_2+y_1'+y_2'\]\[y_2''=5y_1+2y_2+5y_1'y_2'\]\(y_1(0)=y_2(0)=y_1'(0)=4\), \(y_2'(0)=4\)
RolyPoly
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0Note that I put this under linear algebra.

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

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

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

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

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

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

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

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

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

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

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

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

vf321
 3 years 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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