Find the solution of the differential equation that satisfies the given initial condition. {dy} /...

Question:

Find the solution of the differential equation that satisfies the given initial condition.

{eq}\displaystyle \dfrac {dy} {dx} = \dfrac {x \sin x} {y},\ y (0) = -1 {/eq}

Separable Differential Equations:

Differential equations come in many different forms, whenever we can separate a differential equation so that only one of the variables appears on either side of the equals sign, we call it separable. We can solve a separable differential equation by first separating the variables, and then integrating both sides. This gives us a general solution, in order to find a particular solution we must have an initial condition.

Answer and Explanation: 1

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Our differential equation is nice and separable. We separate and integrate to find

{eq}\begin{align*} \frac{dy}{dx} &= \frac{x\sin x}y \\ y\ dy &=...

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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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