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You are implementing the system $$\pmatrix{\ddot x_1\\\ddot x_2} = \pmatrix{1&1\\-4&2} \pmatrix{x_1\\x_2}$$ in its first-order version with $v_k=\dot x_k$. It is not surprising that this different system results in different solutions. For your stated system you would have to use def V(u,t): x1, x2 = u return np.array([ (x1+x2), (4*x1-2*x2)...