Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

UnkleRhaukus

  • one year ago

(3x-2y)dy+(x+y-5)dx=0

  • This Question is Closed
  1. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\newcommand \p \newcommand \p \dd [1] { \,\mathrm d#1 } % infinitesimal \p \de [2] { \frac{ \mathrm d #1}{\mathrm d#2} } % first order derivative \small\begin{align} (3x-2y)\dd y+(x+y-5)\dd x &=0 \\ \de yx &=\frac{5-x-y}{3x-2y} \\ \\ \text{let } x=X+p \\ y=Y+q \\ \de yx=\de YX \\ \\ \de YX &=\frac{5-(X+p)-(Y+q)}{3(X+p)-2(Y+q)} \\ \de YX &=\frac{-X-Y+(5-p-q)}{3X-2Y+(3p-2q)} \\ \\ 5-p-q=0 &\to q=5-p \\ 3p-2q=0 &\to 3p-2(5-p)=0 \to 5p-10=0 &\to p=2 \\ 5-2-q=0 &\to 3-q=0 \to q=3 \\ \\ \de YX &=\frac{-X-Y}{3X-2Y} \\ \de YX &=\frac{-1-Y/X}{3-2Y/X} \\ \\ \text{let }Y/X=V \\ Y=VX \\ Y'=V'X+V \\ \\ V'X+V &=\frac{-1-V}{3-2V} \\ V'X &=\frac{-1-V}{3-2V}-V\frac{3-2V}{3-2V} \\ V'X &=\frac{2V^2-4V-1}{3-2V} \\ \frac{3-2V}{2V^2-4V-1}\dd V &=\frac{\dd X}X \\ \int\frac{1}{2V^2-4V-1}\dd V +\int\frac{2-2V}{2V^2-4V-1}\dd V &=\int\frac{\dd X}X \\ \int\frac{1}{(\sqrt2V-\sqrt2)^2-3}\dd V -\frac12\int\frac{4V-4}{2V^2-4V-1}\dd V &=\int\frac{\dd X}X \\ -\frac13\int\frac{1}{1-\left(\sqrt{\tfrac23}(V-1)\right)^2}\dd V -\tfrac12\ln|2V^2-4V-1| &=\ln|X|+c \\ -\tfrac13\sqrt{\tfrac32}\tanh^{-1}\left(\sqrt{\tfrac23}(V-1)\right) -\tfrac12\ln|2V^2-4V-1| &=\ln|X|+c \\ -\tfrac1{\sqrt6}\tanh^{-1}\left(\sqrt{\tfrac23}\big(\tfrac{y-3}{x-2}-1\big)\right) -\tfrac12\ln\left|2(\tfrac{y-3}{x-2})^2-4(\tfrac{y-3}{x-2})-1\right| &=\ln|x-2|+c \end{align} \]

  2. Psymon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Checking answer? O.o

  3. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is there a more elegant method ?

  4. zzr0ck3r
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol

  5. pgpilot326
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    subtract, integrate and then solve for y

  6. Psymon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Probably not. I would have done basically the same thing except I might have done it right off the bat. y = vx and dy = v'x + vx' and went from there.

  7. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    'x=dx/dx=1

  8. agentc0re
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, there isn not. :( in my opinion this is one of those problems best left to a computer. :) http://www.wolframalpha.com/input/?i=(3x-2y)dy%2B(x%2By-5)dx%3D0&t=crmtb01

  9. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's a question from a second year university differential equations course tutorial week 1

  10. Psymon
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Seems pretty standard, really. Wish I could say Ive seen one of those y = vx dy = v'x + vx' subs that was pretty.

  11. glewis15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it looks like you drew an ostrich

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.