Basic concepts of ODEs. ODEs of first order, separable ODEs and ODEs which can be reduced to those. Exact ODEs of first order and Euler multipliers. Linear ODEs of first order, Bernoulli and Riccati ODEs. Applications: modeling and solving problems from different scientific fields using ODEs of first order. Qualitative analysis of the solutions of ODEs using graphs. Orthogonal trajectories. Picard’s theorem for the existence and uniqueness of the solution of the initial value problem y’ (x)=f(x,y), y(x_0)=y_0. General theory of linear ODEs of order n≥2. Solving linear homogeneous and non-homogeneous ODEs of order n≥2 with constant coefficients. Euler-Cauchy ODEs and techniques for solving ODEs of second order with non-constant coefficients. Applications:  forced and unforced oscillations and additional problems using ODEs of order n≥2. Linear systems of two coupled first order ODEs.

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