Initial value problem

**Apprentice123** · November 9th 2010, 09:14 AM

Solve numerically using Euler's method the following Initial value problem
$y' = 2t - e^{-2t} + 4$
$y(0) = 1$

Use an integration step equal to 0.05s, obtaining the numerical solution for five consecutive steps. Determine the analytic solution

**Apprentice123** · November 9th 2010, 10:58 AM

I used the formula:
$y_{j+1} = y_j +hf(x_j,y_j)$

In this case $x_j$ is $t_j$

$h = 0.05$
$y(0) = 1$
What is the value of $t_0$ ? is equal 0 ?

**Apprentice123** · November 10th 2010, 02:42 PM

My idea is right? What I did is right?

**badgerigar** · November 10th 2010, 11:22 PM

What is the value of

? is equal 0 ?

Since $y$ is a function of $t$ , $y(0)=1$ means that when $t=0$ , $y=1$ . So yes, $t_0=0$

**Apprentice123** · November 11th 2010, 12:33 PM

Originally Posted by badgerigar

Since $y$ is a function of $t$ , $y(0)=1$ means that when $t=0$ , $y=1$ . So yes, $t_0=0$

OK. Thanks

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