ODE Calculator-ODE Solving and Analysis

Example

Given dy/dx + y = x, the calculator can determine the integrating factor, apply it to both sides, and integrate to find the general solution.

Scenario

This function is particularly useful in modeling exponential growth or decay, such as radioactive decay or population growth in biology.

Example

For the equation d^2y/dx^2 - dy/dx - 6y = 0, the calculator identifies the characteristic equation, solves for its roots, and constructs the solution based on the type of roots (real, distinct, or complex).

Scenario

Useful in mechanical and civil engineering for analyzing oscillations, such as in spring-mass systems or in designing stable structures.

Example

For a system like dy/dx = 3x + 4y, dz/dx = -2x + y + z, the tool can apply methods such as matrix exponentiation or eigenvalue-eigenvector approach to find the solution.

Scenario

Important in modeling interconnected systems in ecology, economics, or electrical circuits where multiple variables interact.