# Diff. eq. solve linear equation

• Jtechguy21
In summary, the conversation discusses solving a linear differential equation and correcting a mistake in calculating the integrating factor. The correct integrating factor is x^(1/3).
Jtechguy21

## Homework Statement

Solve the following differential equations.

3xy'+y=12

## Homework Equations

I believe this is a linear equation problem. So I believed to have solved it, however I am not sure if I have done so correctly.

## The Attempt at a Solution

If you're not sure, take the derivative and you can verify it from the equation given. The only mistake I see is in calculating your integrating factor:

When you have $e^{\frac{1}{3}lnx}$, you have to move the 1/3 into the exponent on the $lnx$ before you cancel the e and the ln.

jackarms said:
If you're not sure, take the derivative and you can verify it from the equation given. The only mistake I see is in calculating your integrating factor:

When you have $e^{\frac{1}{3}lnx}$, you have to move the 1/3 into the exponent on the $lnx$ before you cancel the e and the ln.

I see what you mean. so when the e and the ln cancel out, i should be left over with x^(1/3) as my integrating factor correct?

Yes, that looks right. That should give you the right answer.

## 1. What is a differential equation?

A differential equation is a mathematical equation that relates a function to its derivatives. It describes how a function changes over time or in relation to other variables.

## 2. What is a linear equation?

A linear equation is an algebraic equation that contains only variables raised to the first power and constants. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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

To solve a differential equation, you must first determine the type of equation it is (e.g. linear, separable, exact, etc.). Then, you can use various methods such as separation of variables, substitution, or integrating factors to find the solution.

## 4. What is the order of a differential equation?

The order of a differential equation is the highest derivative present in the equation. For example, a first-order differential equation contains only first derivatives, while a second-order differential equation contains second derivatives.

## 5. Are there any applications for solving linear differential equations?

Yes, there are many applications for solving linear differential equations in fields such as physics, engineering, economics, and biology. Some common applications include modeling population growth, analyzing electrical circuits, and predicting the motion of objects.

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