Solve ODEs analytically and numerically with Laplace transforms and eigenvalue analysis.
npx skills add https://github.com/jpfielding/claude.pnge --skill diff-equations
Please help me install this Agent Skill. Skill: diff-equations Source: https://github.com/jpfielding/claude.pnge/tree/main/skills/diff-equations Command: npx skills add https://github.com/jpfielding/claude.pnge --skill diff-equations
This Skill tackles the complex task of solving ordinary differential equations (ODEs), which are fundamental to modeling dynamic systems in engineering and science, by providing both analytical and numerical solution methods.
Use the diff-equations skill to solve the ODE y'' + 4*y = sin(t) with initial conditions y(0)=0 and y'(0)=1.
High-intent search queries and answers about installing and using this skill.
To solve a second-order ODE with constant coefficients, this Skill provides analytical solutions using undetermined coefficients and variation of parameters, handling both homogeneous and non-homogeneous cases with specified initial conditions.
When analytical ODE methods are intractable, the best way to approximate the solution is using numerical methods like Euler's method or the 4th-order Runge-Kutta (RK4) method, both of which this Skill implements for simulating dynamic system profiles.
Yes, you can use Laplace transforms to solve differential equations. The Skill transforms ODEs into algebraic equations in the s-domain and then transforms the solution back to the time domain.
Yes, this Skill supports phase plane analysis for 2x2 linear systems. It classifies equilibrium points such as nodes, spirals, and saddles using eigenvalue methods to help you understand dynamic system behavior.
To solve a system of ODEs using eigenvalue methods, the Skill performs eigenvalue analysis on the system's coefficient matrix, deriving analytical solutions that characterize dynamic behavior for engineering and physics models.
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