Mathematics - Differential Equations - Systems of differential equations - Solve Systems

8 problems: (1-2) Write as matrix system and find eigenvalues: x'=3x+y, y'=x+3y; x'=-x+2y, y'=2x-y. (3-4) Solve using eigenvalues/eigenvectors. (5) Classify the equilibrium (node/saddle/spiral) based on eigenvalues. (6) Apply initial condition x(0)=(1,0) to find c₁,c₂. (7) 'Predator-prey: x'=2x-xy,