I think the differential equations work

maths/differential_equations/solve_first_order_ode.py

@@ -6,6 +6,8 @@ import numpy as np
 from scipy.integrate import solve_ivp
 from typing import Callable, List, Tuple, Dict, Any, Union
 import matplotlib.pyplot as plt
+from maths.differential_equations.ode_interface_utils import parse_float_list, parse_time_span, string_to_ode_func
+import gradio as gr
 
 ODEFunc = Callable[[float, Union[np.ndarray, List[float]]], Union[np.ndarray, List[float]]]
 
@@ -60,3 +62,34 @@ def solve_first_order_ode(
             'success': False,
             'plot_path': None
         }
+    # --- Gradio Interface for First-Order ODEs ---
+first_order_ode_interface = gr.Interface(
+    fn=lambda ode_str, t_span_str, y0_str, t_eval_count, method: solve_first_order_ode(
+        string_to_ode_func(ode_str, ('t', 'y')),
+        parse_time_span(t_span_str),
+        parse_float_list(y0_str), # y0 can be a list for systems
+        int(t_eval_count),
+        method
+    ),
+    inputs=[
+        gr.Textbox(label="ODE Function (lambda t, y: ...)",
+                   placeholder="e.g., lambda t, y: -y*t  OR for system lambda t, y: [y[1], -0.1*y[1] - y[0]]",
+                   info="Define dy/dt or a system [dy1/dt, dy2/dt,...]. `y` is a list/array for systems."),
+        gr.Textbox(label="Time Span (t_start, t_end)", placeholder="e.g., 0,10"),
+        gr.Textbox(label="Initial Condition(s) y(t_start)", placeholder="e.g., 1 OR for system 1,0"),
+        gr.Slider(minimum=10, maximum=1000, value=100, step=10, label="Evaluation Points Count"),
+        gr.Radio(choices=['RK45', 'LSODA', 'BDF', 'RK23', 'DOP853'], value='RK45', label="Solver Method")
+    ],
+    outputs=[
+        gr.Image(label="Solution Plot", type="filepath", show_label=True, visible=lambda res: res['success'] and res['plot_path'] is not None),
+        gr.Textbox(label="Solver Message"),
+        gr.Textbox(label="Success Status"),
+        gr.JSON(label="Raw Data (t, y values)", visible=lambda res: res['success']) # For users to copy if needed
+    ],
+    title="First-Order ODE Solver",
+    description="Solves dy/dt = f(t,y) or a system of first-order ODEs. " \
+                "WARNING: Uses eval() for the ODE function string - potential security risk. " \
+                "For systems, `y` in lambda is `[y1, y2, ...]`, return `[dy1/dt, dy2/dt, ...]`. " \
+                "Example (Damped Oscillator): ODE: lambda t, y: [y[1], -0.5*y[1] - y[0]], y0: 1,0, Timespan: 0,20",
+    flagging_mode="manual"
+)