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#1 2015-02-06 18:14:48

Math1
Member
Registered: 2015-02-06
Posts: 6

Differential Equation - Is this solution correct?

Form for first order linear differential equation:


   and   

Step 1: Substitute
   and   


Step 2: Factor the parts involving v

Step 3: Put the v term equal to zero


Step 4: Solve using separation of variables to find u


   Make   





Step 5: Substitute u back into the equation at Step 2

Step 6: Solve this to find v



Integration by parts






Step 7: Substitute into y = uv to find the solution to the original equation

   Make   

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#2 2015-02-06 18:52:57

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differential Equation - Is this solution correct?

Hi Math1;

I am not getting that. Have you tried plugging your solution back into the DE?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2015-02-06 19:39:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Differential Equation - Is this solution correct?

EM guys check their answers!


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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#4 2015-02-07 04:12:30

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Differential Equation - Is this solution correct?

hi Math1

Welcome to the forum.

This step using integration by parts isn't correct.


Integration by parts

Rather

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#5 2015-02-07 09:29:21

Math1
Member
Registered: 2015-02-06
Posts: 6

Re: Differential Equation - Is this solution correct?

Thanks,
Found formula: The intergration of exponential functions

Integration by substitution







Put   
   back again

Formula:

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#6 2015-02-07 10:00:08

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Differential Equation - Is this solution correct?

There is a much simpler way to do that DE.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2015-02-07 12:24:53

Math1
Member
Registered: 2015-02-06
Posts: 6

Re: Differential Equation - Is this solution correct?

Revision1:
Step 6: Solve this to find v
Integration by parts






Step 7: Substitute into   
   to find the solution to the original equation




Derivative:


Test:
Let   





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