Matematikk 2BHjem

CMD + K

Kapittel 4 · DifferensialligningerODE systems

Second-Order ODE as a First-Order System

0:59Fortellerstemme
0:00 / 0:00

A linear second-order ODE y'' + p y' + q y = 0 becomes a first-order system in two unknowns by introducing v = y'. The state vector (y, v) evolves under a single 2×2 matrix, opening up every first-order tool — Euler, RK4, eigenvector analysis.

second-order ODEfirst-order systemstate vectorcompanion matrixphase plane
ForutsetterEuler's Method: Tangent Steps Along a Slope Field
Neste