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# Solving this Differential Equation watch

1. Solve

Let

Now the differential equation can be written as which simplifies to

So

where to go from here?
2. Divide across, then integrate, by the looks of things.
3. separate variables
4. (Original post by + polarity -)
Divide across, then integrate, by the looks of things.
So

How to integrate RHS?
5. well RHS is same as z^3/(z^4 +1) dz
the top is close to the derivative of the bottom
6. (Original post by TheEd)
So

How to integrate RHS?
Would it become... ? Which =

Ah! Use the trick MrGreedy alluded to!
7. (Original post by + polarity -)
Would it become... ?

Ouch. You could try partial fractions, but I have no idea if it would work.
it's
8. (Original post by + polarity -)
Would it become... ?

Ah! Use the trick MrGreedy alluded to!
all you need to know is that
(integral sign) f'(z)/f(z) dz = ln(f(z)) + c
9. (Original post by MrGreedy)
well RHS is same as z^3/(z^4 +1) dz
the top is close to the derivative of the bottom
So ?
10. (Original post by TheEd)
So ?
yes
11. (Original post by Pheylan)
it's
Yes that's what I got when MrGreedy reminded me of the derivative trick
12. (Original post by Pheylan)
it's
I edited my post.
13. (Original post by TheEd)
Yes that's what I got when MrGreedy reminded me of the derivative trick
i got to the stage but i forgot the trick myself
14. (Original post by MrGreedy)
yes
So

I get

The question also tells me to verify the solution. How would I verify if this is correct?
15. (Original post by TheEd)
So

I get
you have to integrate 1/x as well
16. (Original post by MrGreedy)
you have to integrate 1/x as well
Doh yes forgot about integating LHS!
17. (Original post by MrGreedy)
you have to integrate 1/x as well
So I now get . How would I verify that this is correct?
18. (Original post by TheEd)
So I now get . How would I verify that this is correct?
substitute it back into the original differental equation
19. (Original post by MrGreedy)
substitute it back into the original differental equation
Damn can't get it to verify! Must be wrong!
20. (Original post by MrGreedy)
substitute it back into the original differental equation
When I'm down to this stage:

how would I get rid of the mod signs?

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