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Solving a differential equation with natural log

4

$begingroup$

I am given:

$xdfracdydx=dfrac1y^3$

After separating and integrating, I have:

$y^4/4=ln x+C$

I am supposed to solve this equation, but I'm stuck here. Should I solve explicitly so I can keep $C$?

EDIT:

A solution I came up with last night was:

$y=(4ln x+C)^1/4$

ordinary-differential-equations

share|cite|improve this question

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  don't forget the negative fourth root.
  $endgroup$
  – Stefan Smith
  Jan 16 '14 at 2:46
  

  
  
  
  

add a comment | 

4

$begingroup$

I am given:

$xdfracdydx=dfrac1y^3$

After separating and integrating, I have:

$y^4/4=ln x+C$

I am supposed to solve this equation, but I'm stuck here. Should I solve explicitly so I can keep $C$?

EDIT:

A solution I came up with last night was:

$y=(4ln x+C)^1/4$

ordinary-differential-equations

share|cite|improve this question

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  don't forget the negative fourth root.
  $endgroup$
  – Stefan Smith
  Jan 16 '14 at 2:46
  

  
  
  
  

add a comment | 

$begingroup$

I am given:

$xdfracdydx=dfrac1y^3$

After separating and integrating, I have:

$y^4/4=ln x+C$

I am supposed to solve this equation, but I'm stuck here. Should I solve explicitly so I can keep $C$?

EDIT:

A solution I came up with last night was:

$y=(4ln x+C)^1/4$

ordinary-differential-equations

share|cite|improve this question

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

$endgroup$

share|cite|improve this question

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

share|cite|improve this question

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

edited Jan 15 '14 at 20:45

BaronVT

11.6k11337

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

asked Jan 15 '14 at 20:36

westhe32ndwesthe32nd

198213

1 Answer
1

active

oldest

votes

1

$begingroup$

Try differentiating to see if you got the correct solution!

You can compute
$$
fracdydx = frac14left(4 ln x + Cright)^-3/4left(frac4xright) = frac1xleft(4 ln x + Cright)^-3/4
$$

so
$$
xfracdydx = left(4 ln x + Cright)^-3/4.
$$

Is this equal to $dfrac1y^3$?

share|cite|improve this answer

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

$endgroup$

add a comment | 

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1

$begingroup$

Try differentiating to see if you got the correct solution!

You can compute
$$
fracdydx = frac14left(4 ln x + Cright)^-3/4left(frac4xright) = frac1xleft(4 ln x + Cright)^-3/4
$$

so
$$
xfracdydx = left(4 ln x + Cright)^-3/4.
$$

Is this equal to $dfrac1y^3$?

share|cite|improve this answer

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

$endgroup$

add a comment | 

1

$begingroup$

Try differentiating to see if you got the correct solution!

You can compute
$$
fracdydx = frac14left(4 ln x + Cright)^-3/4left(frac4xright) = frac1xleft(4 ln x + Cright)^-3/4
$$

so
$$
xfracdydx = left(4 ln x + Cright)^-3/4.
$$

Is this equal to $dfrac1y^3$?

share|cite|improve this answer

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

$endgroup$

add a comment | 

$begingroup$

Try differentiating to see if you got the correct solution!

You can compute
$$
fracdydx = frac14left(4 ln x + Cright)^-3/4left(frac4xright) = frac1xleft(4 ln x + Cright)^-3/4
$$

so
$$
xfracdydx = left(4 ln x + Cright)^-3/4.
$$

Is this equal to $dfrac1y^3$?

share|cite|improve this answer

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

$endgroup$

share|cite|improve this answer

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337