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- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.05%3A_Separable_EquationsThis page discusses separable differential equations, emphasizing identification, variable separation, and the integration process for solutions. It addresses implicit solutions, their importance, cha...This page discusses separable differential equations, emphasizing identification, variable separation, and the integration process for solutions. It addresses implicit solutions, their importance, challenges in deriving explicit forms, and includes examples demonstrating the method.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/06%3A_Spectral_Theory/6.06%3A_Dynamical_SystemsIn this section we consider discrete dynamical systems and how the techniques of linear transformations covered in previous sections can be used to find solutions.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_II%3A_Integral_Calculus/05%3A_Introduction_to_Differential_EquationsA goal of this chapter is to develop solution techniques for different types of differential equations. As the equations become more complicated, the solution techniques also become more complicated, ...A goal of this chapter is to develop solution techniques for different types of differential equations. As the equations become more complicated, the solution techniques also become more complicated, and in fact an entire course could be dedicated to the study of these equations. In this chapter we study several types of differential equations and their corresponding methods of solution.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_Equations/2.06%3A_Pursuit_CurvesThis page discusses pursuit curves involving a hawk chasing a sparrow on the y-axis. It derives equations that relate the hawk's interception path to both its and the sparrow's speeds. By solving a di...This page discusses pursuit curves involving a hawk chasing a sparrow on the y-axis. It derives equations that relate the hawk's interception path to both its and the sparrow's speeds. By solving a differential equation, the hawk's trajectory is determined, revealing that the hawk can successfully catch the sparrow if it travels faster than the sparrow.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.06%3A_Linear_Equations_and_the_Integrating_FactorOne of the most important types of equations we will learn how to solve are the so-called linear equations. In fact, the majority of the course is about linear equations. In this lecture we focus on t...One of the most important types of equations we will learn how to solve are the so-called linear equations. In fact, the majority of the course is about linear equations. In this lecture we focus on the first order linear equation.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/06%3A_Systems_of_ODEs/6.01%3A_Introduction_to_Systems_of_ODEsOften we do not have just one dependent variable and just one differential equation, we may end up with systems of several equations and several dependent variables even if we start with a single equa...Often we do not have just one dependent variable and just one differential equation, we may end up with systems of several equations and several dependent variables even if we start with a single equation.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/01%3A_First_Order_ODEs/1.10%3A_Numerical_Methods_-_Eulers_MethodThis page elaborates on Euler's method for approximating solutions to differential equations when closed-form solutions are not feasible. It discusses the method's iterative approach and its first-ord...This page elaborates on Euler's method for approximating solutions to differential equations when closed-form solutions are not feasible. It discusses the method's iterative approach and its first-order accuracy, noting the error reduction with smaller step sizes. The text also addresses challenges like numerical instability and the importance of selecting appropriate methods and step sizes.
- https://math.libretexts.org/Courses/De_Anza_College/Introductory_Differential_Equations/02%3A_Applications_of_First_Order_Equations/2.02%3A_Cooling_ProblemsThis section deals with applications of Newton's law of cooling and with mixing problems.
