Explore a comprehensive series of lectures on differential equations covering a wide range of topics. Begin with linear, exact, and homogeneous differential equations, then progress to Bernoulli equations and substitution methods. Learn about applications of first-order linear differential equations and linear models. Dive into the theory of linear equations, reduction of order, and constant coefficient equations with distinct, repeated, and complex roots. Study undetermined coefficients, variation of parameters, and Cauchy-Euler equations. Examine applications in spring-mass systems and power series solutions. Investigate the method of Frobenius, Bessel and Legendre equations, Laplace transforms, and their properties. Conclude with linear systems of differential equations, including repeated eigenvalues and phase portraits.