
DE URGENT Help
Ok, I have to solve this using a computer program but if someone can just explain the question to me that would be a start.
y'(t)=20y+e^t
Solve for 0£t£10 using the forward Euler with timestep 0.1, i.e. write the derivative in terms of y(t) and y(t+dt), with the time set to t on the right hand side, and solve y(t+dt) to set up the update scheme.
I've read up on the Euler's forward scheme but still don't understand what the question is asking or how to go about it!

$\displaystyle \mathsf{f(t,y)=\frac{dy}{dt}=20y+e^{t}}$
Eulers method basically boils down to:
$\displaystyle \mathsf{y_{i+1}=y_i+f(y_i,t_i)\cdot \Delta t}$
Where your $\displaystyle \mathsf{\Delta t}$ is your time step and each forward y value is calculated from the current time t, the current y value and the time step.
For the specific case you've stated:
$\displaystyle \mathsf{y_{i+1}=y_i+\left(20y_i+e^{t_i}\right)\cdot \Delta t}$
If put that into a spreadsheet with an initial value for y when t=0 it'll produce the estimated values

Ok for the backward one my tutor gave me this
y=(y+dt e^(n dt))/(1+20 dt)
I don't understand how he's got that. Any ideas?

Well for a backwards step approach the equation just becomes:
$\displaystyle \mathsf{y_{i1}=y_if(y_i,t_i)\cdot \Delta t}$ and needs an initial value for y when t=10.
I'm not really sure what the n represents in that equation, I may have learnt the method with different notation to the way your tutor is teaching it.