Question

Determine if the differential equation is separable, and if so, write it in the form $h(y) d y=g(x) d x$. $$y^{\prime}=x e^{y}$$

Name: Problem 2, Chapter 11: Calculus Single Variable
Uploaded: 2021-04-24T08:49:43-08:00
Duration: 28 s
Channel: Vikash Ranjan
Description: Determine if the differential equation is separable, and if so, write it in the form h(y) d y=g(x) d x. y^'=x e^y

   Determine if the differential equation is separable, and if so, write it in the form $h(y) d y=g(x) d x$.
$$y^{\prime}=x e^{y}$$

Calculus Single Variable

Deborah… 7th Edition

Chapter 11, Problem 2

Instant Answer

Solved by Expert Vikash Ranjan

04/24/2021

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A differential equation is said to be separable if it can be written in the form $h(y) d y=g(x) d x$. Show more…

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Determine if the differential equation is separable, and if so, write it in the form $h(y) d y=g(x) d x$. $$y^{\prime}=x e^{y}$$

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Key Concepts

Separable Differential Equations

A separable differential equation is one that can be rewritten so that all terms involving one variable (and its differential) are on one side of the equation and all terms involving the other variable are on the opposite side. This property allows the equation to be integrated with respect to each variable independently.

Method of Separation of Variables

This method involves algebraic manipulation of the differential equation to isolate the functions of each variable on opposite sides of the equation, typically in a form such as h(y)dy = g(x)dx. The resulting separated equation is then integrated on both sides to find the general solution.

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