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# Ode watch

1. Hi , I have this equation y Prime=-y+t+1
my question am not sure if we integrate how did it become y=t+e^-t

y prime is dy/dt

this question is from euler's method

thanks
2. (Original post by meme12)
Hi , I have this equation y Prime=-y+t+1
my question am not sure if we integrate how did it become y=t+e^-t

y prime is dy/dt

this question is from euler's method

thanks
Thread will be moved to the maths study help sub-forum where you will get a much faster answer.

Thanks.
3. (Original post by meme12)
Hi , I have this equation y Prime=-y+t+1
my question am not sure if we integrate how did it become y=t+e^-t

y prime is dy/dt

this question is from euler's method

thanks
Head moved for the above reason
4. Removed, been completely dumb here using the wrong method, I'm not too knowledgeable about Euler's Method, but I'm sure someone here can help you, sorry !

Euler's Method, however is an approximation, you've given the exact solution, which I assumed was found via solving it using an integrating factor.

Here's what I proviously wrote:

Spoiler:
Show

If you are aware of the integrating factor, we can come to the conclusion (from the top of my head via inspection):

Hence

I assume the boundary condition is

5. (Original post by meme12)
Hi , I have this equation y Prime=-y+t+1
my question am not sure if we integrate how did it become y=t+e^-t

y prime is dy/dt

this question is from euler's method

thanks
If you want to find an exact solution, then use an integrating factor and solve the O.D.E normally, then I assume there are some initial conditions, which enable you to deduce that the constant of integration is 1.

Euler's method involves setting up an iterative formula to give an approximation to the solution, this one's a little more complicated than other examples I've seen, but I'll give it a shot. . .
If you write then you can show that

This assumes that you use a constant change in time, for each step.
You then have an iterative formula in the form:

Using any initial conditions you have, you may then be able to write in terms of , and find any point specified, without further information, there's not a lot I can say
6. Thanks for the try , I am not sure how did we get that answer but I will try to ask
7. (Original post by meme12)
Thanks for the try , I am not sure how did we get that answer but I will try to ask
The answer is exact, as I and joostan mentioned. Euler's method is an approximation, it's not exact. Hence its just solved a first order DE, by the integrating factor. I assumed it gave you some initial conditions, which would need to be or such. Can you post the full question?
8. (Original post by meme12)
Thanks for the try , I am not sure how did we get that answer but I will try to ask
I'm guessing you want to know how to get the exact answer without using Euler's method?

For the general method, you can see the notes here: http://tutorial.math.lamar.edu/Class...rConcepts.aspx

First you solve the homogeneous part of the equation to get the complimentary function as

Next you look for a particular solution of the form . Plug this into your original equation to get . From inspection of equating coefficients, we see that and .

The general solution of the ode is given by adding the complimentary and the particular solution to give . To find the value of the constant you need an initial condition which I assume you were given as .
9. Ok what about solving it using first order did equa that what my tutor said what is the difference?
10. (Original post by meme12)
Ok what about solving it using first order did equa that what my tutor said what is the difference?
Thanks
11. This way seem more easier , I will try this way any idea what is the dif between using this way and solve first order differential equation way under linear equation

thank you
12. Will you do this same way . I will try tonputcas much as I can from question
y prime =1/t(y^2-y)
y(1)=1/2

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