Procedure

1. Enter the Differential Equation

   • Type the first-order ODE in terms of y'.
   • Ensure that ‘x’ is used as the independent variable and ‘y’ as the dependent variable.

2. Set Initial Conditions

   • Provide the initial x value (x₀).
   • Enter the corresponding initial y value (y₀) at that point.
   • These values are essential to compute the power series coefficients.

3. Configure Simulation Parameters

   • Specify the desired range for x over which the solution will be plotted.
   • Select the number of terms to be used in the power series expansion (more terms = better accuracy).

4. Run the Simulation

   • Click the Simulate button.
   • The tool will compute the coefficients of the power series and generate the approximate ODE solution.

5. View the Output

   • Observe the series solution displayed textually on the right side of the interface.
   • Examine the plotted solution curve to visualize how the function behaves over the specified range.

6. Analyze and Compare

   • Check how the number of series terms affects accuracy and smoothness of the solution.
   • Try solving different ODEs from the given examples to compare solution characteristics.
   • Assess how the power series approximation performs near and away from the expansion point.