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[✓] Solve and Plot numerically this differential equation?

GROUPS:

Consider the following code:

e1 = 0.001;
e^0.4 = {{2.37/de^0.06} - 1.6}/10 {1 - Log[de]/13.8}^0.7

the initial value is e1=0.001 for t0=1 and the time period is between {t,1,18000}

POSTED BY: dimitriss mal
Answer
5 months ago

Your equation is implicit in the derivative. We can work around the problem by taking the derivative of the equation, which makes it explicit in the second derivative. If I don't misunderstand your syntax, here is an attempt:

eq = e[t]^(4/10) == (((237/100)/e'[t]^ (6/100)) - 
     16/10)/(10 (1 - Log[e'[t]]/(138/10))^(7/100))
deq = Simplify@D[eq, t]
de1 = e'[1] /. 
   Solve[eq /. {t -> 1} /. e[1] -> 1/1000, e'[1], Reals][[1]] // N
sol = NDSolveValue[{deq, e[1] == 1/1000, e'[1] == de1}, 
  e, {t, 1, 18000}]
Plot[sol[t], {t, 1, 18000}]
POSTED BY: Gianluca Gorni
Answer
5 months ago

Thank you very much for your aswer!!!it works perfect!!!!

POSTED BY: dimitriss mal
Answer
4 months ago

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