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Find {eq}f {/eq}. Given {eq}\displaystyle f''(x) = x^{-2},\ x \gt 0,\ f(1) = 0,\ f(6) = 0 {/eq}.

Question:

Find {eq}f {/eq}. Given {eq}\displaystyle f''(x) = x^{-2},\ x \gt 0,\ f(1) = 0,\ f(6) = 0 {/eq}.

Separable Differential Equation

The differential equation is said to be separable if we can be able to separate the variables in the equation. In other words, we can rearrange the equation so that all the terms that has only one variable are in one side while the terms that contains other variable are on the other side of the equation.

Answer and Explanation: 1

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First, we let

{eq}\displaystyle g(x) = f'(x) \quad (1) \\ \\ \displaystyle \Rightarrow g'(x) = f''(x) \quad (2) {/eq}

So that the differential...

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Separable Differential Equation: Definition & Examples

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Chapter 16 / Lesson 1
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Discover what separable differential equations are and their uses. Learn to identify if an equation is separable and how to solve them through given examples.


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