I missed the lecture and the text book goes over this very quickly...

This is an autonomous and therefore separable equation so

If I have done this right, what is the next step? If not please correct :$

Thank You

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- Mar 24th 2009, 07:27 PMLenInitial Value Problem
I missed the lecture and the text book goes over this very quickly...

This is an autonomous and therefore separable equation so

If I have done this right, what is the next step? If not please correct :$

Thank You - Mar 24th 2009, 09:37 PMChris L T521
It all is correct so far. Just keep in mind that y is the subject of the equation. So we can rewrite what you have as . Note that if you complete the square, you end up with , where is another constant.

Now, applying the initial condition , we have

Therefore,

Does this make sense? - Mar 24th 2009, 09:55 PMLen
- Mar 25th 2009, 03:12 AMGrandadInitial Value Problem