PLS, some one help me find the 1st 4 iterates using Picard's iteration.

[manttiz]

Question

Use Picard's iteration to find the first 4 iterates of solutions of the problem dx/dt = -tx, x(0) = 1.

If anyone can help me solve this, I'll be so grateful. I wait anxiously to get the solution.

 

[berkeman]

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[manttiz]

I'm finding it impossible to write the equations here, though the clue can be gotten at http://www.cse.uiuc.edu/eot/modules/ode/picard/

 

[HallsofIvy]

If you have the differential equation dx/dt= f(x,t) with x(t₀)= x₀ then "Picard's interation", used in his proof of the existence of solutions of the initial value problem, is
$$x(t)= \int_{t_0}^t f(x,t)dt+ x_0$$
starting with x(t)= x₀ and then using the resulting x(t) in the next iteration.

Here, f(x,t)= -tx and x(0)= x₀= 1 so the first "iteration" is
[tex]\int_0^t -tdt+ 1[/itex]
Surely you can continue from there.