I am having a difficulty fixing the error I’m encountering in my program. I keep getting this error that the y0 is null and I’ve tried everything but the error persists. I’m using Apache Netbeans as my programming tool.

Here is the complete code:

import javax.script.ScriptEngine;
import javax.script.ScriptEngineManager;
import javax.script.ScriptException;
import java.util.Scanner;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.analysis.solvers.NewtonRaphsonSolver;

public class NewtRaphNonLinear {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        // Prompting user to input equations
        System.out.print("Enter equation 1 (in terms of x and y): ");
        String equation1 = scanner.nextLine();
        System.out.print("Enter equation 2 (in terms of x and y): ");
        String equation2 = scanner.nextLine();

        // Prompting user to input initial guesses
        System.out.print("Enter initial guess for x and y: ");
        double x0 = scanner.nextDouble();
        double y0 = scanner.nextDouble(); // Declare y0 without final

        // Prompting user to input relative error
        System.out.print("Enter relative error: ");
        double relativeError = scanner.nextDouble();

        // Using Apache Commons Math library for solving equations
        NewtonRaphsonSolver solver = new NewtonRaphsonSolver();
        UnivariateDifferentiableFunction systemFunction = new UnivariateDifferentiableFunction() {
            @Override
            public double value(double point) {
                double x = point; // Extract x from the point
                double y = point; // Extract y from the point
                return evaluateEquation(x, y, equation1, equation2);
            }


            @Override
            public DerivativeStructure value(DerivativeStructure t) throws UnsupportedOperationException {
                return null;
           }
        };

        // Solving equations
        double solutionX = solver.solve(100, systemFunction, x0, relativeError);
        double solutionY = evaluateEquation(solutionX, y0, equation1, equation2);

        System.out.println("Solution:");
        System.out.println("x = " + solutionX);
        System.out.println("y = " + solutionY);
    }

    // Function to evaluate equations
    private static double evaluateEquation(double x, double y, String equation1, String equation2) {
        // Replace 'x' and 'y' in the equations with their values
        String replacedEquation1 = equation1.replaceAll("x", "(" + x + ")").replaceAll("y", "(" + y + ")");
        String replacedEquation2 = equation2.replaceAll("x", "(" + x + ")").replaceAll("y", "(" + y + ")");

        // Evaluate the expressions using ScriptEngineManager
        double result1 = evaluateExpression(replacedEquation1);
        double result2 = evaluateExpression(replacedEquation2);

        return result1 - result2; // Returns the difference for the Newton-Raphson solver
    }

    // Function to evaluate mathematical expressions
    private static double evaluateExpression(String expression) {
        ScriptEngineManager mgr = new ScriptEngineManager();
        ScriptEngine engine = mgr.getEngineByName("JavaScript");
        try {
            return (double) engine.eval(expression);
        } catch (ScriptException e) {
            e.printStackTrace();
            return Double.NaN;
        }
    }
}

The equations I’m using is this:
Enter equation 1 (in terms of x and y): x^2+2y^2=22
Enter equation 2 (in terms of x and y): 2x^2-xy+3y=11
Enter initial guess for x and y: 1.5 2.5
Enter relative error: 0.01

I’ve expected the result to be:
Solution: (Approximately)
x = 2.000000002808708
y = 3.0000000001706063

but the actual result is this:
Exception in thread “main” java.lang.NullPointerException: Cannot invoke “org.apache.commons.math3.analysis.differentiation.DerivativeStructure.getValue()” because “y0” is null