Introduction:
The Milne predictor-correction method is a numerical method used to solve ordinary differential equations. It involves predicting the value of the dependent variable at the next point using an extrapolation formula, and then correcting this prediction using a correction formula. This process is repeated iteratively until the desired accuracy is achieved.

Given Differential Equation:
The given differential equation is dy/dx = x - y^2.

Milne Predictor-Correction Method:
The Milne predictor-correction method involves the following steps:

Step 1: Initialization:
- Given the initial values of x0 and y0, where y0 is the value of y at x0.
- In this case, the table is not provided, so we have to assume the initial values. Let's assume x0 = 0 and y0 = 0.

Step 2: Predictor Step:
- Using the initial values, we can predict the value of y at the next point, y1, using the following formula:
y1 = y0 + h/3 * (4f(x0, y0) - f(x0-h, y0-2hf(x0, y0)))

Step 3: Correction Step:
- We can correct the predicted value of y using the following formula:
y1_corrected = y0 + h/3 * (f(x0+h, y1) + 4f(x0, y0) + f(x0-h, y0-2hf(x0, y0)))

Step 4: Repeat:
- Repeat steps 2 and 3 iteratively until the desired accuracy is achieved.

Calculation:
Let's calculate the value of y at the next point using the Milne predictor-correction method.

- Given x0 = 0, y0 = 0, and the correct answer is 0.305.
- Let's assume the step size h = 0.1.

Iteration 1:
- Using the predictor formula, we can calculate:
y1 = 0 + 0.1/3 * (4(0) - (0-0.2*(0)^2))
= 0 + 0.1/3 * (0 + 0)
= 0

- Using the correction formula, we can calculate:
y1_corrected = 0 + 0.1/3 * ((0+0.1) - 0 + 4(0) + (0-0.2*(0)^2))
= 0 + 0.1/3 * (0.1 + 0 + 0)
= 0

Iteration 2:
- Using the predictor formula, we can calculate:
y2 = 0 + 0.1/3 * (4(0) - (0-0.2*(0)^2))
= 0 + 0.1/3 * (0 + 0)
= 0

- Using the correction formula, we can calculate:
y2_corrected = 0 + 0.1/3 * ((0+0.2) - 0 + 4(0) + (0-0.2*(0)^