DiffEqFundamental Matrix

Fundamental Matrix for Linear Systems

Build Φ(t) = [eˡ¹ᵗv₁ | eˡ²ᵗv₂] for X′ = AX, verify Φ′ = AΦ, compute Φ(0)⁻¹, and solve the IVP X(t) = Φ(t)·Φ(0)⁻¹·X₀.

Live Calculator · Step-by-Step · Differential Equations

Matrix A and Initial Conditions

Matrix A =

[

]

x₁(0) = X₀₁

x₂(0) = X₀₂

Results

Eigenvalues & Eigenvectors

—

Φ(t) — Fundamental Matrix

—

Φ(0)⁻¹

—

General Solution X(t) = Φ(t)·C

—

Particular Solution with ICs

—

Step-by-Step Work

Your solution will appear here.

Solution Components x₁(t) and x₂(t) on [0, 5]