Web Reference: Watch the following video to see the worked solution to Example: Solving an Initial-Value Problem and the above Try It. In calculus, an initial value problem[a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Assume that f and g are continuous functions on an interval I. Then for each x0 2 I and for all y0 2 R, the initial value problem y 0 = f(x)y + g(x) y(x0) = y0 has exactly one solution y = '(x) on the interval I. Example : Solve the initial value problem y 0 = xy with y(0) = 1. Note : This equation is linear with integrating factor
YouTube Excerpt: This calculus video tutorial explains how to solve the

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Differential Equations: Lecture 1.1-1.2 Definitions and Terminology and Initial Value Problems
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Solving an Initial Value Problem with Laplace Transforms y' + 4y = e^(4t)
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