The problem I have is the initial value problem

${y}^{\u2034}=x+y$

with

$y(1)=3,{y}^{\prime}(1)=2,{y}^{\u2033}(1)=1$

that should be solved with Eulers method using the step length, $h=\frac{1}{2}$.

The iteration step for Eulers method is ${y}_{n+1}={y}_{n}+hf({x}_{n},{y}_{n})$. So I should need a system of equations of my initial values I have. I started with substituting:

${U}_{1}=y,{U}_{2}={y}^{\prime},{U}_{3}={y}^{\u2033}$

and then

${U}_{1}^{\prime}={U}_{2},{U}_{2}^{\prime}={U}_{3},{U}_{3}^{\prime}=x+{U}_{1}$

And it's here I'm stuck, I don't understand how I should start iterate with the step-length from here, I have only encounteblack first-order problem with Eulers method so I would love if someone could point me in the right direction.