differential-equations

What I do

• Solve first-order ODEs (separable, linear, exact)
• Solve higher-order linear ODEs with constant coefficients
• Apply Laplace transforms for ODE solutions
• Solve systems of differential equations
• Analyze stability of equilibrium solutions
• Solve partial differential equations

When to use me

When modeling dynamic systems, physics problems, or any system involving rates of change.

Key Concepts

• First-Order Linear: dy/dx + P(x)y = Q(x), integrate factor μ = e^{∫Pdx}
• Separable: dy/dx = f(x)g(y), ∫dy/g(y) = ∫f(x)dx
• Second-Order Linear: ay'' + by' + cy = 0, characteristic r² + br/a + c/a = 0
• Laplace Transform: L{f(t)} = ∫₀^∞ e^{-st}f(t)dt, converts ODEs to algebraic
• Particular Solution: Sum of homogeneous + particular solves full equation
• Phase Lines: Visualize equilibrium stability for autonomous ODEs