Solve the given differential equation by separation of variables. x (d y)/(d x)=4 y

Name: Problem 9, Chapter 8: Calculus, Early Transcendentals
Uploaded: 2021-07-09T18:44:46-08:00
Duration: 58 s
Channel: Edward Downes
Description: Solve the given differential equation by separation of variables. x (d y)/(d x)=4 y

step 1 Okay, we're solving this differential equation using separation of variables. We're going to get

Solve the given differential equation by separation of...

Key Concepts

Exponentiation

Exponentiation is the process of raising a number or expression to a power, which is a critical step when solving equations that involve logarithms. After integrating and obtaining a logarithmic expression, exponentiating both sides of the equation helps to isolate the original variable and obtain the general solution.

Integration

Integration is a fundamental mathematical technique used for finding antiderivatives or the accumulation of quantities. In the context of differential equations, once the variables are separated, integration is used to obtain an implicit or explicit form of the solution by incorporating an integration constant, which represents the generality of the solution.

Separable Differential Equations

Separable differential equations are a class of differential equations in which the variables can be separated on different sides of the equation. This separation allows the equation to be rearranged so that one side contains only the dependent variable and its differential, while the other side contains only the independent variable and its differential, making it possible to integrate both sides independently.

Differential Equation

A differential equation is a mathematical equation that relates a function and its derivatives. It is used to describe various phenomena in science and engineering by establishing a connection between an unknown function and its rates of change.

Separation of Variables

The separation of variables is a method used to solve differential equations that can be written in a separable form. By isolating each variable with its corresponding differential, the equation becomes two integrals that can be computed separately, thereby leading to the solution of the original equation.

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