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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
 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
 one year ago

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

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

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

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

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

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

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

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

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

sirm3dBest ResponseYou've already chosen the best response.0
how about laplace transform?
 one year ago

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

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

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

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

vf321Best 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.
 one year ago
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