Summary

Adds an initial, modular differential-equation solving slice for the compute engine:

• registers symbolic DSolve in the calculus library
• implements symbolic first-order linear scalar ODE solving in src/compute-engine/symbolic/differential-equations.ts
• registers numeric NDSolve in the calculus library
• implements fixed-step scalar RK4 support in src/compute-engine/numerics/differential-equations.ts
• adds focused tests for symbolic solutions, unsupported inert cases, RK4 sample accuracy, and a Gaussian IVP with a non-elementary antiderivative checked against Erf

Scope / Limitations

This is intentionally narrow so the API and result shape can get feedback before broader ODE support is added.

Current symbolic support handles first-order linear equations of the form y'(x) + p(x)y(x) = q(x) and leaves unsupported/nonlinear/higher-order equations inert.

Current numeric support handles explicit scalar first-order IVPs with fixed-step RK4 and returns sample data as a List of [x, y] pairs. It does not yet implement adaptive RK45, systems, interpolation objects, stiff solvers, implicit equations, or higher-order reductions.

Validation

• node_modules/.bin/jest.cmd --config ./config/jest.config.cjs test/compute-engine/differential-equations.test.ts --runInBand --reporters default
• node_modules/.bin/jest.cmd --config ./config/jest.config.cjs test/compute-engine/calculus.test.ts --runInBand --reporters default --testNamePattern DERIVATION
• node_modules/.bin/madge.cmd --circular --extensions ts src/compute-engine
• node_modules/.bin/tsc.cmd --target es2022 --module es2022 --moduleResolution bundler --types node --skipLibCheck -d --allowImportingTsExtensions true --emitDeclarationOnly --ignoreConfig --outDir .typecheck ./src/compute-engine.ts