Differential Equations: Solutions and Monotonicity

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Explores finding solutions of differential equations, emphasizing maximal solutions and general solutions with constants.

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Covers the material point model, initial conditions, and Newton's laws in physics.

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Covers Fourier series, periodic functions, and Fourier transforms.

Covers separable differential equations of order 1, defining separable equations and providing examples.

Covers linear first order differential equations, separation of variables, particular solutions, uniqueness, and coefficients application.

Covers solutions of differential equations with initial conditions and boundedness concepts.

Covers the definition and properties of non-constant functions and equations of order 4.