A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
Solve the differential equation 14y'= x + y
by making the change of variable u = x + y.
 one year ago
Solve the differential equation 14y'= x + y by making the change of variable u = x + y.

This Question is Closed

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large 14\color{royalblue}{\frac{dy}{dx}}=\color{orangered}{x+y}\] \[\large \color{orangered}{u=x+y}\]\[\large \frac{du}{dx}=1+\frac{dy}{dx} \qquad \rightarrow \qquad \color{royalblue}{\frac{dy}{dx}=\frac{du}{dx}1}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Understand how to plug in the substitution? :) I colorcoded it to make it a little easier.

dillpickles
 one year ago
Best ResponseYou've already chosen the best response.0Sorry but I am still confused. I understand where everything came from but what do i do from where you left off? Do I write 14du/dx1=u?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Yes very good! :) We can use prime notation if it's a little easier to understand,\[\large 14(u'1)=u\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1From here, distribute the 14 to each term in the brackets. Then you can solve it either by separation of variables, or by getting it into standard form and finding an integrating factor.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1I hope this step wasn't too confusing, \(\large \frac{du}{dx}=1+\frac{dy}{dx}\) It's the same as \(\large u'=1+y'\) I was just trying to emphasize that we're taking the derivative with respect to x. That's what the Leibniz notation was showing us.

dillpickles
 one year ago
Best ResponseYou've already chosen the best response.0No, I understand that. I just have a hard time solving them on my own. Thanks

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Cool c: Lemme know if you get stuck.
Ask your own question
Ask a QuestionFind 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.