Is This the Correct Method for Solving Differential Equations on Midterms?

What do your trusty differentiation skills tell you?In summary, the conversation is about a question from a midterm and the correct method or answer for it. The conversation also touches on using differentiation skills and integrating with respect to x.
  • #1
lyj0211
2
0
Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.
 

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  • #2
What do your trusty differentiation skills tell you? Where did f(x) come from?
 
  • #3
SteamKing said:
What do your trusty differentiation skills tell you? Where did f(x) come from?

this is my answer, I am just not sure if it is correct.
 
  • #4
It's correct, I think.
 
  • #5
lyj0211 said:
this is my answer, I am just not sure if it is correct.

Does that mean that you don't know how to differentiate the function you've found and check whether it satisfies the original equation?
 
  • #6
lyj0211 said:
Hi, this question came up in my midterm and I was hoping to know if this is the correct method or answer.

You know you're immediately going to integrate with respect to [itex]x[/itex], so you can conserve symbols by writing "[itex]u_x = \dfrac{(\frac 23 t^3 + t)}{1 + x} + f'(x)[/itex] for an arbitrary differentiable [itex]f(x)[/itex]".
 

1. What are differential equations?

Differential equations are mathematical equations that involve the derivatives of one or more variables. They are used to describe the relationship between a variable and its rate of change over time.

2. Why are differential equations important?

Differential equations are important in many fields of science and engineering, as they can be used to model and predict the behavior of complex systems. They are also used to solve real-world problems, such as in physics, chemistry, biology, and economics.

3. How do I solve a differential equation?

The methods for solving differential equations vary depending on the type of equation. Some common techniques include separation of variables, substitution, and using integrating factors. It is important to first classify the type of differential equation before selecting a method to solve it.

4. What are the applications of differential equations?

Differential equations have numerous applications in different fields such as predicting population growth, modeling the spread of diseases, understanding climate change, and designing control systems for engineering applications. They are also used in data analysis and machine learning algorithms.

5. Is knowledge of calculus necessary to understand differential equations?

Yes, a solid understanding of calculus is essential for understanding differential equations. Differential equations involve derivatives, which are a fundamental concept in calculus. It is also important to have a good understanding of algebra and basic mathematical concepts to solve differential equations.

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