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