Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

dillpickles

  • 3 years ago

Solve the differential equation 14y'= x + y by making the change of variable u = x + y.

  • This Question is Closed
  1. zepdrix
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\large 14\color{royalblue}{\frac{dy}{dx}}=\color{orangered}{x+y}\] \[\large \color{orangered}{u=x+y}\]\[\large \frac{du}{dx}=1+\frac{dy}{dx} \qquad \rightarrow \qquad \color{royalblue}{\frac{dy}{dx}=\frac{du}{dx}-1}\]

  2. zepdrix
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Understand how to plug in the substitution? :) I color-coded it to make it a little easier.

  3. dillpickles
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry 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/dx-1=u?

  4. zepdrix
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes very good! :) We can use prime notation if it's a little easier to understand,\[\large 14(u'-1)=u\]

  5. zepdrix
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    From 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.

  6. zepdrix
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I 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.

  7. dillpickles
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, I understand that. I just have a hard time solving them on my own. Thanks

  8. zepdrix
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Cool c: Lemme know if you get stuck.

  9. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy