Dtjytyk

What does it mean that physics no longer uses mechanical models to describe phenomena?

What is "gratricide"?

What is the appropriate index architecture when forced to implement IsDeleted (soft deletes)?

Performance gap between vector<bool> and array

How do living politicians protect their readily obtainable signatures from misuse?

Is it possible for SQL statements to execute concurrently within a single session in SQL Server?

Hangman Game with C++

What initially awakened the Balrog?

Maximum summed subsequences with non-adjacent items

How much damage would a cupful of neutron star matter do to the Earth?

What are the diatonic extended chords of C major?

What was the first language to use conditional keywords?

What is this clumpy 20-30cm high yellow-flowered plant?

Do any jurisdictions seriously consider reclassifying social media websites as publishers?

How to write this math term? with cases it isn't working

Taylor expansion of ln(1-x)

Chinese Seal on silk painting - what does it mean?

How come Sam didn't become Lord of Horn Hill?

Central Vacuuming: Is it worth it, and how does it compare to normal vacuuming?

Do wooden building fires get hotter than 600°C?

Trademark violation for app?

Converted a Scalar function to a TVF function for parallel execution-Still running in Serial mode

Is grep documentation about ignoring case wrong, since it doesn't ignore case in filenames?

Effects on objects due to a brief relocation of massive amounts of mass

Solving a differential equation with natural log

4

$begingroup$

I am given:

$xdfrac{dy}{dx}=dfrac{1}{y^3}$

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:

$xdfrac{dy}{dx}=dfrac{1}{y^3}$

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:

$xdfrac{dy}{dx}=dfrac{1}{y^3}$

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
$$
frac{dy}{dx} = frac{1}{4}left(4 ln x + Cright)^{-3/4}left(frac{4}{x}right) = frac{1}{x}left(4 ln x + Cright)^{-3/4}
$$

so
$$
xfrac{dy}{dx} = left(4 ln x + Cright)^{-3/4}.
$$

Is this equal to $dfrac{1}{y^{3}}$?

share|cite|improve this answer

answered Jan 15 '14 at 20:49

BaronVTBaronVT

11.6k11337

$endgroup$

add a comment | 

Your Answer

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f639668%2fsolving-a-differential-equation-with-natural-log%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

1

$begingroup$

Try differentiating to see if you got the correct solution!

You can compute
$$
frac{dy}{dx} = frac{1}{4}left(4 ln x + Cright)^{-3/4}left(frac{4}{x}right) = frac{1}{x}left(4 ln x + Cright)^{-3/4}
$$

so
$$
xfrac{dy}{dx} = left(4 ln x + Cright)^{-3/4}.
$$

Is this equal to $dfrac{1}{y^{3}}$?

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
$$
frac{dy}{dx} = frac{1}{4}left(4 ln x + Cright)^{-3/4}left(frac{4}{x}right) = frac{1}{x}left(4 ln x + Cright)^{-3/4}
$$

so
$$
xfrac{dy}{dx} = left(4 ln x + Cright)^{-3/4}.
$$

Is this equal to $dfrac{1}{y^{3}}$?

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
$$
frac{dy}{dx} = frac{1}{4}left(4 ln x + Cright)^{-3/4}left(frac{4}{x}right) = frac{1}{x}left(4 ln x + Cright)^{-3/4}
$$

so
$$
xfrac{dy}{dx} = left(4 ln x + Cright)^{-3/4}.
$$

Is this equal to $dfrac{1}{y^{3}}$?

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