Dy/dx = xe^(y-2x), form differntial eqaution

The steps to get to the answer likely involved integrating both sides and then solving for y.How to get the answer? To get the answer, you will need to integrate both sides of the differential equation and then solve for y. You can start by integrating the term xe^(y-2x) with respect to x and then solving for y. You can also check your solution by taking the derivative of your answer and seeing if it equals the original differential equation.In summary, the given equation is already a differential equation. The provided answer is likely the solution to the differential equation after integrating both sides and solving for y. To get the answer, you will need to integrate both sides and solve for y, and then check your solution by taking the
  • #1
john augustine
1
0
dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation . the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) + a , how to get the answer? btw , i have attached my working

BpjWSZj.jpg
 
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  • #2
Hi John, :welcome:

You really want to
  • post in the homework forum
  • use the template
  • read and follow the guidelines
I hope this reaches you before the mentors lash out: What's the difference between your solution and the given / book solution ?
 
  • #3
I moved the thread to our homework section.

Check your integration of 2x e2x, for example by calculating the derivative of what you used as integral.
 
  • #4
john augustine said:
dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation .
The equation you wrote already is a differential equation.
john augustine said:
the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) +a
Based on the answer, the problem seems to be asking you to solve the differential equation.
 

Related to Dy/dx = xe^(y-2x), form differntial eqaution

1. What does "Dy/dx" mean in this equation?

"Dy/dx" is a notation used in calculus to represent the derivative of a function y with respect to x. It represents the rate of change of y with respect to x.

2. How do you solve this differential equation?

To solve a differential equation such as this one, you can use techniques such as separation of variables, integrating factors, or substitution. The specific method used will depend on the form of the equation and any initial conditions given.

3. What is the significance of "e" in this equation?

"e" is a mathematical constant approximately equal to 2.718. It is the base of the natural logarithm and often appears in equations involving exponential growth or decay.

4. Can this equation be applied to real-world situations?

Yes, this equation can be applied to real-world situations, such as modeling population growth or chemical reactions. It represents a relationship between two variables, and the solution to the equation can provide insight into the behavior of these variables.

5. Are there any limitations to this equation?

Like any mathematical model, this equation may have limitations in its ability to accurately represent real-world situations. It may not account for all factors or variables that could affect the relationship between x and y. Additionally, the solution to the equation may have a limited range of validity.

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