# Initial value problem

• Nov 9th 2010, 09:14 AM
Apprentice123
Initial value problem
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
• Nov 9th 2010, 10:58 AM
Apprentice123
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 ?
• Nov 10th 2010, 02:42 PM
Apprentice123
My idea is right? What I did is right?
• Nov 10th 2010, 11:22 PM
Since $y$ is a function of $t$, $y(0)=1$ means that when $t=0$, $y=1$. So yes, $t_0=0$
Since $y$ is a function of $t$, $y(0)=1$ means that when $t=0$, $y=1$. So yes, $t_0=0$