Math & Numbers
Second-Order ODE Solver (Characteristic Equation)
Solve a·y'' + b·y' + c·y = f(x): characteristic roots, three homogeneous cases, undetermined coefficients with resonance, and C1/C2 from initial conditions.
text· Text resultOpen tool
Quick start
Call this tool from your code in three languages.
cURL
curl -X POST 'https://api.elysiatools.com/en/api/tools/second-order-ode-solver' \
-H 'Content-Type: application/json' \
-d '{"a":1,"b":-3,"c":2,"forcing":"none","constantF":1,"polyCoeffs":"1","expA":1,"expK":1,"sinA":1,"sinB":0,"sinK":1,"x0":0,"y0":1,"y0prime":0}'API reference
Send a POST request with your inputs as JSON. File parameters require a separate upload first.
Endpoint
HTTP
POST https://api.elysiatools.com/en/api/tools/second-order-ode-solverParameters
| Name | Type | Required | Description |
|---|---|---|---|
| a | number | Yes | Coefficient of y'' (must be nonzero). |
| b | number | Yes | Coefficient of y'. |
| c | number | Yes | Coefficient of y. |
| forcing | select | Yes | — |
| constantF | number | No | Used when forcing = Constant. |
MCP integration
Add this tool to your Model Context Protocol server so AI agents can list and call it.
Server configuration
Add this block to your MCP client configuration:
mcp.json
{
"mcpServers": {
"elysiatools-second-order-ode-solver": {
"name": "second-order-ode-solver",
"description": "Solve a·y'' + b·y' + c·y = f(x): characteristic roots, three homogeneous cases, undetermined coefficients with resonance, and C1/C2 from initial conditions.",
"baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=second-order-ode-solver",
"command": "",
"args": [],
"env": {},
"isActive": true,
"type": "sse"
}
}
}List available tools
After connecting to the SSE endpoint, list the exposed tools:
tools/list
{
"jsonrpc": "2.0",
"id": 1,
"method": "tools/list"
}Call this tool
Invoke the tool by its id, passing arguments built from its parameters:
tools/call
{
"jsonrpc": "2.0",
"id": 2,
"method": "tools/call",
"params": {
"name": "second-order-ode-solver",
"arguments": {
"a": 1,
"b": -3,
"c": 2,
"forcing": "none",
"constantF": 1,
"polyCoeffs": "1",
"expA": 1,
"expK": 1,
"sinA": 1,
"sinB": 0,
"sinK": 1,
"x0": 0,
"y0": 1,
"y0prime": 0
}
}
}Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).
Questions or issues? Contact [email protected]