Question

$\frac{d y}{d x}=e^{3 x+2 y}$

Name: Problem 7, Chapter 2: Advanced Engineering Mathematics
Uploaded: 2021-12-23T07:05:31-08:00
Duration: 43 s
Channel: Hast Aggarwal
Description: (d y)/(d x)=e^3 x+2 y

   $\frac{d y}{d x}=e^{3 x+2 y}$

Advanced Engineering Mathematics

Dennis G. Zill,… 5th Edition

Chapter 2, Problem 7

Instant Answer

Solved by Expert Hast Aggarwal

12/23/2021

Step 1

We can do this by multiplying both sides by $e^{-2y}$ and dividing both sides by $e^{3x}$, which gives us $e^{-2y} dy = e^{3x} dx$. Show more…

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$\frac{d y}{d x}=e^{3 x+2 y}$

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Key Concepts

Separable Differential Equations

A separable differential equation is one that can be written in the form dy/dx = f(x)g(y), which allows one to rearrange the equation by isolating the y terms with dy and the x terms with dx on opposite sides. This is a key method for solving first-order differential equations by integrating both sides separately.

Exponential Functions

Exponential functions involve expressions where the variable is in the exponent, such as e^(3x) or e^(2y). Understanding the laws of exponents allows one to split or combine these expressions, which is especially useful when they are part of separable differential equations.

Integration

Integration is the process of finding the antiderivative of a function and is critical in solving differential equations. Once the variables in a separable differential equation are separated, both sides are integrated with respect to their own variables to find a general solution.

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