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June 3rd, 2012, 01:52 AM   #1
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differential equation use substitution methode

for this equation i use substitution methode.
but my answer is not right. dont know where i make a mistake, please someone can help me to check. thanks!

right answer is y=4x ln(cx)
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June 3rd, 2012, 02:43 AM   #2
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Re: differential equation use substitution methode

i have an other question




last step i dont get it, where is u' and +u get from? what is the u'?
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June 3rd, 2012, 02:50 AM   #3
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Re: differential equation use substitution methode

U=Y*1/x+4
x*U-4=Y

Its the mistake in your previous question
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June 3rd, 2012, 03:05 AM   #4
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Re: differential equation use substitution methode

x*y'=y+4*x
x*dy=y*dx+4x*dx
x*dy-y*dx=4x*dx
(x*dy-y*dx)/(x^2) = (4/x)*dx
d(y/x) = (4/x)*dx, integrating both sides,
y/x+c1 = 4ln(x)+c2
y=4xln(x)+Cx where C=c1-c2

My C = your 4ln(c)
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June 3rd, 2012, 03:49 AM   #5
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Re: differential equation use substitution methode

Quote:
Originally Posted by mathbalarka
U=Y*1/x+4
x*U-4=Y

Its the mistake in your previous question
thanks alot mathbalarka for helping me out. do you know this question?

Quote:
Originally Posted by zell^
i have an other question




last step i dont get it, where is u' and +u get from? what is the u'?
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June 3rd, 2012, 04:03 AM   #6
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Re: differential equation use substitution methode

[color=#000000]What mathbalarka has done.....

remember that , now for



.[/color]
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June 3rd, 2012, 04:16 AM   #7
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Re: differential equation use substitution methode

y'=1-y/x
x*y'=x-y
x*y'+y=x
x*y'+x'*y=x
(xy)'=x
d(xy)=x*dx integrating,
xy+c1=x^2/2+c2
xy=x^2/2+C
y=x/2+C/x
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June 3rd, 2012, 04:21 AM   #8
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Re: differential equation use substitution methode

If you want, I can tell you the solution of
a,b are constants

Note: sorry for writing answers of previous questions without using
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June 3rd, 2012, 08:42 AM   #9
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Re: differential equation use substitution methode

thx problems solved. now got an other one problem. how do i found out C is just C not lnC? how can i recognize it after intergration?
example:


other one



confused
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June 3rd, 2012, 10:02 AM   #10
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Re: differential equation use substitution methode

Quote:
Originally Posted by zell^
thx problems solved. now got an other one problem. how do i found out C is just C not lnC? how can i recognize it after intergration?
example:


other one



confused
Can you explain your question more simply? I cant understand
According to my calculations,
The genarel solution of is:
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