二阶常系数线性微分方程求解器（特征方程法）

POST http://127.0.0.1:3003/zh/api/tools/second-order-ode-solver

{
  "mcpServers": {
    "elysiatools-second-order-ode-solver": {
      "name": "second-order-ode-solver",
      "description": "求解 a·y'' + b·y' + c·y = f(x)：解特征方程 ar² + br + c = 0，按判别式给出齐次解（两相异实根 / 二重根 / 共轭复根），用待定系数法求特解（含共振：k 为特征根时试探解乘 x^m），支持常数、多项式、A·e^(kx) 与 A·sin(kx)+B·cos(kx) 右端项；给定 y(x₀) 与 y'(x₀) 时由 2×2 线性方程组定出 C1、C2。经典例：y''−3y'+2y=0，y(0)=1，y'(0)=0 → y = −e^(2x)+2e^x。",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=second-order-ode-solver",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

{
  "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
}
  }
}