A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Can someone help me solve this Differential equation? dy+lnxy dx=(4x+lny)dx
anonymous
 5 years ago
Can someone help me solve this Differential equation? dy+lnxy dx=(4x+lny)dx

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think this is where I start? \[dy/dx+\ln xy=4x+\ln y\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You just have to use log laws to open the product of xy in the LHS log into a sum. That is,\[\frac{dy}{dx}+\ln xy = 4x + \ln y \rightarrow \frac{dy}{dx}+\ln x + \ln y = 4x + \ln y\]The logs of y cancel and you're left with\[\frac{dy}{dx}=4x\ln x \rightarrow y=2x^2x \ln x +x+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[=2x^2+x(1\ln x)+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you know how to integrate ln(x)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, I'm not too familiar with the laws of logs thats where I needed help. Does dy just = y?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, are you asking if dy becomes y as in \[\frac{dy}{dx}=4x \ln x \rightarrow \int\limits_{}{}dy=\int\limits_{}{}4x\ln x dx \rightarrow \]\[y=2x^2x \ln x + x+c\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Right... and isn't \[\int\limits_{}^{} lnx dx = x\ln(x)x\] ? You have +x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No...\[\int\limits_{}{}\ln x dx=x \ln x x+c\]I have a + because I skipped a step: when you sub. the result of the integral in, you'll have\[2x^2(x \ln x x) +c\]which is equal to \[2x^2x \ln x + x +c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can integrate ln(x) using integration by parts, taking u=ln(x), dv=dx and going from there.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ohh I see I forgot to distribute the  back into it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can always check your solution by subbing it into the differential equation.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok and for the final anwer you just moved the x on the back, to the front and factored a little right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, for the final answer (which technically you don't need to do since the first answers the question), I've just taken out the common factor of x.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Great. Thanks for your help :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.