Solving IVP: Is My Answer Correct?

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In summary, when determining if your answer to an IVP is correct, you should plug the given initial conditions into your solution and substitute it into the differential equation. If the resulting equation is true, then your solution is correct. If your answer is incorrect, you should double check your work and use a different method to solve the problem. It is also possible to use a calculator to solve an IVP, but it is important to enter all equations and initial conditions correctly. The method used to solve an IVP depends on the type of differential equation, and an IVP can only have one unique solution due to the use of initial conditions to determine constants of integration.
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squenshl
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I had to solve an IVP:
[tex]\partial[/tex]/[tex]u\partial[/tex]t + 4[tex]\partial[/tex]u/[tex]\partial[/tex]x = e2x, u(x,0) = f(x).
I got an answer of u = 1/2 +f(x-4t).
Is this correct and if not, where did I go wrong.
 
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Hard to tell where you went wrong without seeing your work. But it isn't correct for at least two reasons:

1. It doesn't satisfy u(x,0) = f(x) (although it would without the 1/2).
2. If you plug it into the DE you get 0, not e(2x).
 

FAQ: Solving IVP: Is My Answer Correct?

How do I know if my answer to an IVP is correct?

To determine if your answer to an IVP is correct, you can use the following steps:

  • Plug the given initial conditions into your solution
  • Substitute the solution into the given differential equation
  • If the resulting equation is true, then your solution is correct

What should I do if my answer to an IVP is incorrect?

If your answer to an IVP is incorrect, you should double check your work and make sure all calculations are accurate. You can also try solving the problem using a different method to see if you get the same result. If you are still unsure, it is always a good idea to seek assistance from a professor or tutor.

Can I use a calculator to solve an IVP?

Yes, you can use a calculator to solve an IVP. However, it is important to make sure your calculator is set to the correct mode (e.g. radians or degrees) and that you enter all equations and initial conditions correctly.

How do I know which method to use to solve an IVP?

The method you use to solve an IVP depends on the type of differential equation given. Some common methods include separation of variables, integrating factors, and using series solutions. Consult your textbook or professor for guidance on which method to use for a specific problem.

Is it possible for an IVP to have more than one solution?

No, an IVP can only have one unique solution. This is because the initial conditions given in an IVP are used to determine the constants of integration in the solution, making it a unique solution for that specific problem.

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