You want a question based on the given formula and Runge-Kutta method example? Here's one:

Question 5:
Use the fourth-order Runge-Kutta (RK4) method to approximate the value of $y(0.2)$ for the differential equation
$\frac{dy}{dx} = 1 - x + 4y$
with the initial condition $y(0) = 1$, step size $h = 0.1$.

Would you like further details or additional guidance on solving this? Here are related follow-up questions:

1. What are the key steps in the Runge-Kutta method?
2. Why is the RK4 method considered more accurate than simpler methods like Euler's method?
3. How do you compute each intermediate slope ($K_1$, $K_2$, $K_3$, $K_4$)?
4. What happens if the step size ($h$) is reduced by half in this method?
5. Can the RK4 method handle stiff equations effectively?

Tip: The RK4 method is particularly useful for its balance of computational efficiency and accuracy in solving ordinary differential equations.