Please help with this differential equation

In summary, the conversation discusses a discrepancy between the speaker's answer and the textbook answer. The respondent explains that the solution is still correct and can be confirmed by taking the derivative. They also mention the importance of an initial value constraint to make the solution unique. Finally, the speaker thanks the respondent for pointing out their mistake regarding the constant term.
  • #1
rxfudd
4
0
I cannot figure out where I am going wrong. My answer and the textbook answer are different by a negative sign. Can someone review my work and tell me what I am doing wrong?
 

Attachments

  • diffeq.jpg
    diffeq.jpg
    17.8 KB · Views: 433
Physics news on Phys.org
  • #2
Why do you think, your solution is wrong? It's perfectly right! It's the general solution of the equation (I've not checked it, but this you can do by taking the derivative and check whether it fulfills your equation), and whether you call the integration constant [itex]-C_3[/itex] or [itex]C[/itex] doesn't matter.

The solution is made unique by giving, e.g., an initial value [itex]y(0)=y_0[/itex] as a constraint. If you use this in your and the textbook's answer you'll get the same result by choosing the right [itex]C_3[/itex] and [itex]C[/itex] to match the initial-value constraint, respectively.
 
  • #3
Ah yes, the constant...the (x2+4)-4 term can be positive or negative because of the constant.

Thank you for reviewing my work and pointing that out. Amateur mistake :)
 

1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It describes how a quantity changes over time or space, and is commonly used in physics, engineering, and other scientific fields to model real-world processes.

2. How do I solve a differential equation?

There are various methods for solving differential equations, including separation of variables, integrating factors, and using power series. The most appropriate method depends on the specific type of differential equation and its initial conditions.

3. What are the applications of differential equations?

Differential equations have many applications in science and engineering, including modeling population growth, describing fluid dynamics, and predicting the motion of objects in space. They are also used in economics, biology, and other fields to analyze and understand complex systems.

4. Can computers solve differential equations?

Yes, computers can solve differential equations using numerical methods such as Euler's method, Runge-Kutta methods, and finite difference methods. These methods use a series of calculations to approximate the solution to a differential equation.

5. How can I check if my solution to a differential equation is correct?

You can check your solution to a differential equation by plugging it back into the original equation and seeing if it satisfies the equation. You can also use software or online tools to graph your solution and compare it to the original equation's graph.

Similar threads

  • Differential Equations
Replies
3
Views
2K
  • Differential Equations
Replies
2
Views
915
  • Differential Equations
Replies
5
Views
922
  • Differential Equations
Replies
3
Views
1K
  • Differential Equations
Replies
4
Views
1K
  • Differential Equations
Replies
25
Views
2K
Replies
2
Views
2K
  • Differential Equations
Replies
3
Views
2K
  • Differential Equations
Replies
12
Views
1K
  • Differential Equations
Replies
4
Views
1K
Back
Top