# Find the largest interval which includes x = 0 for which the given initial value problem has a...

## Question:

Find the largest interval which includes x = 0 for which the given initial value problem has a unique solution.

{eq}\displaystyle (x - 4) y'' + 2 y = x,\ y (0) = 0,\ y' (0) = 1 {/eq}.

## Second order differential equation:

The second-order differential equation comprises an independent variable, dependent variable, constant, and function itself. Movement of the electron expressed by using differential equations.

## Answer and Explanation:

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Differential equation,

{eq}\left( {x - 4} \right)y'' + 2y = x {/eq}

Convert into standard form,

{eq}y'' + \dfrac{2}{{\left( {x - 4}...

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Chapter 16 / Lesson 3In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.