# Solve DE: (y-1)e^y = [(x^2+1)^(3/2)]/3 + C

• Growl
In summary, the conversation discusses solving the differential equation y' = [x(x^2+1)^1/2]/ye^y. The individual has some difficulty solving for y and the other person suggests isolating x as a possible solution.
Growl
Given that y' = [x(x^2+1)^1/2]/ye^y
How do you find solve the differential equation?
I got through some parts but have hard time solving for y when i got
(y-1)e^y = [(x^2+1)^(3/2)]/3 + C

Thanks a lot :)

Last edited:
It looks like you did a bit of a botch job on integrating the RHS.

$$\int x^3 + xdx = x^4/4 + x^2/2$$

I don't think you can really go much farther than you have.

EDIT: It looks right now. I would probably just hand it in as is, because I don't see a way to solve that

Last edited:
My bad, it's actually y' = [x(x^2+1)^1/2]/ye^y, ;), posted the problem up wrong...

Thanks anyway!

if you want to give your professor something, you can isolate x in that problem, although you'll have a plus or minus in the solution..

## 1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with one or more of its derivatives. It is used to describe how a system changes over time and is a fundamental tool in many scientific fields, including physics, engineering, and economics.

## 2. How do you solve a differential equation?

To solve a differential equation, you need to find the function that satisfies the equation. This can be done through various methods, such as separation of variables, integrating factors, or using a series solution. In this specific case, we can use the method of separation of variables to solve the given differential equation.

## 3. What is the method of separation of variables?

The method of separation of variables involves separating the differential equation into two separate equations and then integrating both sides. This method is used when the differential equation can be written in the form of dy/dx = f(x)g(y), where f(x) is a function of x and g(y) is a function of y.

## 4. How do you apply the method of separation of variables to the given equation?

To apply the method of separation of variables to the given equation, we first rearrange the equation to get it in the form of dy/dx = f(x)g(y). In this case, we can divide both sides by e^y and multiply both sides by dx to get dy = [(x^2+1)^(3/2)]/3e^y dx. Then, we can integrate both sides to get the solution for y.

## 5. What is the general solution to the given differential equation?

The general solution to the given differential equation is y = ln(x^2 + 1) + C, where C is the constant of integration. This solution can be obtained by integrating both sides of the equation and adding the constant of integration to the right side. It represents all possible solutions to the given differential equation.

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