differential-equations-solver

Solve ODEs using techniques for first-order linear and separable equations, second-order constant coefficient equations, and systems of ODEs. This Skill guides you through method selection, derivation steps, and LaTeX-formatted solutions tailored to your equation type.

Laplace transforms convert differential equations into algebraic equations, making them easier to solve. This Skill explains the transform process, applies it to ODE problems, and shows how to convert solutions back to the time domain.

Yes. Set up differential equations for population growth, circuit behavior, heat distribution, and other dynamic systems. This Skill provides step-by-step guidance on formulating the correct equation type and solving it with appropriate methods.

Solve PDEs including the heat equation using separation of variables and boundary-value problem techniques. This Skill explains physical significance, provides step-by-step solutions, and guides method selection for different PDE classes.

Apply numerical methods including Euler and Runge-Kutta algorithms to approximate ODE solutions. This Skill explains each method's accuracy trade-offs, implementation steps, and when to use each approach for engineering and physics problems.

Perform stability analysis on ODE solutions to understand long-term system behavior. This Skill guides equilibrium identification, linearization techniques, and qualitative analysis methods for engineering and physics applications.