- #1
ImAnEngineer
- 209
- 1
Hey guys.
I've recently started studying differential equations. There is one thing I don't understand and of which I simply can't find an explanation.
I'm trying to solve some linear differential equations without using standard solutions.
Say we have the equation:
[tex]\frac{dp}{dt}=0.5p - 450[/tex]
The next step is (according to my book):
[tex](1) \frac{dp}{p-900}=\frac{1}{2} dt[/tex]
All of the next steps that lead to the solution are clear to me. They use the chain rule to integrate, exponentiate, and get: [itex]p=900+ce^\frac{t}{2}[/itex].
But what I don't understand, is why they first write it in the form of eq.(1), and not as, say:
[tex](2) \frac{dp}{.5p-450}=1 dt[/tex] ?
Possibly it's a silly question, but nevertheless, please help me out :) .
I've recently started studying differential equations. There is one thing I don't understand and of which I simply can't find an explanation.
I'm trying to solve some linear differential equations without using standard solutions.
Say we have the equation:
[tex]\frac{dp}{dt}=0.5p - 450[/tex]
The next step is (according to my book):
[tex](1) \frac{dp}{p-900}=\frac{1}{2} dt[/tex]
All of the next steps that lead to the solution are clear to me. They use the chain rule to integrate, exponentiate, and get: [itex]p=900+ce^\frac{t}{2}[/itex].
But what I don't understand, is why they first write it in the form of eq.(1), and not as, say:
[tex](2) \frac{dp}{.5p-450}=1 dt[/tex] ?
Possibly it's a silly question, but nevertheless, please help me out :) .
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