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

1. Feb 15, 2007

### manttiz

Question

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

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

2. Feb 16, 2007

### Staff: Mentor

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3. Feb 16, 2007

### manttiz

4. Feb 16, 2007

### HallsofIvy

Staff Emeritus
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 existance 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.