Numerical Analysis

Solve the following differential equation numerically using two different methods:

i$.$ Forward Euler method.

ii$.$ Backward Euler method.

$y^{}=-2y+x,y(0)=1$

Tasks:

Use Euler's methods with: $h=0\mathrm{.}1$ and $h=0\mathrm{.}05$

For both methods, solve the first $3$ iterations by hand.

$(14$ Mark$)$

For both methods, write a pseudo code.