[ Ссылка ]. Start here if you need Differential Equations in your Calculus 2 course! Differential Equations (Diff Eqs) are introduced by starting with a free fall model and moving to exponential growth of a population. In the first case, the differential equation is a pure antiderivative problem which can be solved by direct integration (for both the velocity and height). Solutions are also vertical translations of each other. In the second case, the differential equation is autonomous. It can be solved either by guessing or with separation of variables. Solutions are horizontal translations of each other. Distinctions are made between specific constants (parameters) and arbitrary constants, and between a general solution of an ODE and a particular (unique) solution to an initial-value problem (IVP). A couple more examples are done by guessing and separation of variables near the end.
Calculus 2, Lecture 30
#DifferentialEquation #DifferentialEquations #calculus2
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(0:00) Fun names for Differential Equations
(1:56) Free fall model with no air resistance
(30:12) Pure antiderivative problems dy/dt = f(t)
(33:52) Example: dy/dt = sin(t), y(0) = 3
(35:12) Population growth model (exponential growth)
(48:02) Autonomous ODEs dy/dt = f(y)
(55:35) Example: Find n so y = x^n solves x*dy/dx - 3y = 0
(1:01:17) Example: Find A and n so so y = A*x^n solves y*dy/dx = 6x^2
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