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I try to solve this equation:

enter image description here

And I got an answer:

DSolve[k'[t] == s k[t]^a - (n + b) k[t], k[t], t]

{{k[t] -> E^(-6 t) C[1]}}

But now I try this:

DSolve[{k'[t] == s k[t]^a - (n + b) k[t], k'[t] == 0}, k[t], t]

And got an error:

DSolve: There are fewer dependent variables than equations, so the system is overdetermined.

Please, help me. What should I do?

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3
  • $\begingroup$ Please provide the values of s,a,n,b. $\endgroup$ Commented Jan 21, 2019 at 15:15
  • 3
    $\begingroup$ you meant k'[0] == 0 (not k'[t] == 0)? $\endgroup$
    – kglr
    Commented Jan 21, 2019 at 15:16
  • $\begingroup$ s = 0.299, a = 0.35, n = 0.01, b = 0.1 $\endgroup$ Commented Jan 21, 2019 at 15:18

1 Answer 1

3
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Try

s = 0.299; a = 0.35; n = 0.01; b = 0.1; 
K = DSolveValue[{k'[t] == s k[t]^a - (n + b) k[t], k[0] == 0}, k ,t] // Chop
(*Function[{t},0.216305 2.71828^(-0.0715 t) (-1. + 1. 2.71828^(0.0715 t))(2.71828^(-0.0715 t) (-299. + 299. 2.71828^(0.0715 t)))^(7/13)]*)

Plot[K[t], {t, 0, 1}, AxesLabel -> {"t", "k[t]"}]

enter image description here

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