Verifying Solution to DE: y' = (1+1/x)y y(1) = e

  • Thread starter frs2fh
  • Start date
In summary, the speaker has solved a first order equation to help a friend and wants to confirm if it is correct. It is an initial value problem and the solution is y = CXe^x with C = 1 for the initial value. The speaker is unsure if they made a mistake and wants reassurance. Another person confirms that the solution is correct and suggests checking it by plugging in y and y' into the equation to see if it works. The speaker is relieved to know that their solution is correct.
  • #1
frs2fh
6
0
Hi,
I have a first order equation I've solved to help a friend along in another poblem. But I have not solved a DE in over 10yrs - so I just want to make sure I did it correct.
It an IVP.

y' = (1+1/x)y y(1) = e.

So I come up with y = CXe^x
(C = 1 for IV)
 
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  • #2
You can easily check it yourself: you have y(x), and can compute y'(x), then plug these into the DE to see if they work.

RGV
 
  • #3
Thanks Ray,
I did this before I posted and it seemed to work. I'm just afraid if I made a mistake in one direction I made it again in the other. Like I stated, I haven't done this (any integration / derivatives or solving DE) in over a decade. I just want to know if it's correct.
 
  • #4
It is correct. ehild
 

1. How do you verify a solution to a differential equation?

To verify a solution to a differential equation, you must substitute the solution into the original equation and see if it satisfies the equation. This means that when you plug in the solution for the dependent variable, the resulting expression should equal the right side of the equation.

2. What is the general process for verifying a solution to a differential equation?

The general process for verifying a solution to a differential equation is to first find the derivative of the solution, then plug it into the original equation. If the resulting expression is equal to the right side of the equation, then the solution is verified.

3. Can a solution to a differential equation be verified using any method?

No, a solution to a differential equation can only be verified by substitution. Other methods, such as integration or differentiation, cannot be used to verify a solution.

4. What do you do if a solution to a differential equation does not satisfy the original equation?

If a solution to a differential equation does not satisfy the original equation, then it is not a valid solution. This means that you must go back and check your work to see where you made a mistake in finding the solution.

5. Why is it important to verify a solution to a differential equation?

It is important to verify a solution to a differential equation because it ensures that the solution is correct and satisfies the original equation. This is crucial in applications of differential equations, as incorrect solutions can lead to incorrect predictions or solutions to real-world problems.

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