# Diff. Eq: Linear Eq. Method: I can't find the mistake I made

• Jeff12341234
In summary, the Linear Equations Method is a technique used to solve first-order differential equations in the form of dy/dx = f(x,y), involving rearranging the equation, integrating with respect to the independent variable, solving for the constant of integration, and substituting initial conditions. Common errors include incorrect rearrangement, integration, and substitution. This method can only be used for certain types of differential equations and tips for avoiding mistakes include double checking, using correct integration techniques, and practicing.
Jeff12341234
I must have made a mistake somewhere in these steps but I don't see it. The answer I got isn't the correct one. Where did I go wrong?

Wow I'm sorry, but that's very hard for me to read. Could you post the question itself along with any initial conditions you were given?

Does this make sense?

You've got the wrong sign on the P(x) you integrated. You did P(x)=2/(x*log(x)). It should be P(x)=(-2/(x*log(x))).

Thanks. I see it.

## 1. What is the Linear Equations Method for solving Differential Equations?

The Linear Equations Method is a technique used to solve first-order differential equations in the form of dy/dx = f(x,y), where f(x,y) is a function of x and y. This method involves rearranging the equation to isolate the differential term, and then integrating both sides with respect to the independent variable.

## 2. What are the steps for solving a Differential Equation using the Linear Equations Method?

Step 1: Rearrange the equation to isolate the differential term.
Step 2: Integrate both sides of the equation with respect to the independent variable.
Step 3: Solve for the constant of integration.
Step 4: Substitute the initial conditions into the solution to find the particular solution.

## 3. Why can't I find the mistake I made in solving a Differential Equation using the Linear Equations Method?

It is possible that there is no mistake in your solution. However, common errors in solving differential equations using the linear equations method include incorrect rearrangement of the equation, incorrect integration, or incorrect substitution of initial conditions.

## 4. Can I use the Linear Equations Method to solve any type of Differential Equation?

No, the Linear Equations Method can only be used to solve first-order differential equations in the form of dy/dx = f(x,y). For other types of differential equations, other methods such as separation of variables or substitution may be required.

## 5. Are there any tips for avoiding mistakes when using the Linear Equations Method?

Yes, here are a few tips to help you avoid mistakes when using the Linear Equations Method:
- Double check your rearrangement of the equation.
- Check your integration and make sure you have used the correct integration techniques.
- Be careful when substituting initial conditions into the solution.
- Practice, practice, practice!

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