Solve the separable differential equation 10 x - 6 y sqrt {x^2 + 1} dy / dx = 0, with the initial...

Question:

Solve the separable differential equation {eq}\displaystyle 10 x - 6 y \sqrt {x^2 + 1}\ \dfrac {dy}{dx} = 0 {/eq}, with the initial condition {eq}y(0) = 4 {/eq}.

Solution of the Differential Equation:

The given differential equation can be solved by separating the equation into two parts. We move all of the equations involving the {eq}y{/eq} variable to one side and all of the equation involving the {eq}x{/eq} variable to the other side, then we can integrate both sides.

$$\displaystyle\int P(y)\: dy=\int Q(x)\: dx $$

Answer and Explanation:

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Consider the differential equation

$$\displaystyle 10 x - 6 y \sqrt {x^2 + 1}\ \dfrac {dy}{dx} = 0,\quad y(0)=4\\ \displaystyle 6 y \sqrt {x^2 + 1}\...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In 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.


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