A community for students.
Here's the question you clicked on:
 0 viewing
UnkleRhaukus
 one year ago
(3x2y)dy+(x+y5)dx=0
UnkleRhaukus
 one year ago
(3x2y)dy+(x+y5)dx=0

This Question is Closed

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1\[\newcommand \p \newcommand \p \dd [1] { \,\mathrm d#1 } % infinitesimal \p \de [2] { \frac{ \mathrm d #1}{\mathrm d#2} } % first order derivative \small\begin{align} (3x2y)\dd y+(x+y5)\dd x &=0 \\ \de yx &=\frac{5xy}{3x2y} \\ \\ \text{let } x=X+p \\ y=Y+q \\ \de yx=\de YX \\ \\ \de YX &=\frac{5(X+p)(Y+q)}{3(X+p)2(Y+q)} \\ \de YX &=\frac{XY+(5pq)}{3X2Y+(3p2q)} \\ \\ 5pq=0 &\to q=5p \\ 3p2q=0 &\to 3p2(5p)=0 \to 5p10=0 &\to p=2 \\ 52q=0 &\to 3q=0 \to q=3 \\ \\ \de YX &=\frac{XY}{3X2Y} \\ \de YX &=\frac{1Y/X}{32Y/X} \\ \\ \text{let }Y/X=V \\ Y=VX \\ Y'=V'X+V \\ \\ V'X+V &=\frac{1V}{32V} \\ V'X &=\frac{1V}{32V}V\frac{32V}{32V} \\ V'X &=\frac{2V^24V1}{32V} \\ \frac{32V}{2V^24V1}\dd V &=\frac{\dd X}X \\ \int\frac{1}{2V^24V1}\dd V +\int\frac{22V}{2V^24V1}\dd V &=\int\frac{\dd X}X \\ \int\frac{1}{(\sqrt2V\sqrt2)^23}\dd V \frac12\int\frac{4V4}{2V^24V1}\dd V &=\int\frac{\dd X}X \\ \frac13\int\frac{1}{1\left(\sqrt{\tfrac23}(V1)\right)^2}\dd V \tfrac12\ln2V^24V1 &=\lnX+c \\ \tfrac13\sqrt{\tfrac32}\tanh^{1}\left(\sqrt{\tfrac23}(V1)\right) \tfrac12\ln2V^24V1 &=\lnX+c \\ \tfrac1{\sqrt6}\tanh^{1}\left(\sqrt{\tfrac23}\big(\tfrac{y3}{x2}1\big)\right) \tfrac12\ln\left2(\tfrac{y3}{x2})^24(\tfrac{y3}{x2})1\right &=\lnx2+c \end{align} \]

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1is there a more elegant method ?

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.0subtract, integrate and then solve for y

Psymon
 one year ago
Best ResponseYou've already chosen the best response.0Probably 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.

agentc0re
 one year ago
Best ResponseYou've already chosen the best response.0No, there isn not. :( in my opinion this is one of those problems best left to a computer. :) http://www.wolframalpha.com/input/?i=(3x2y)dy%2B(x%2By5)dx%3D0&t=crmtb01

UnkleRhaukus
 one year ago
Best ResponseYou've already chosen the best response.1It's a question from a second year university differential equations course tutorial week 1

Psymon
 one year ago
Best ResponseYou've already chosen the best response.0Seems pretty standard, really. Wish I could say Ive seen one of those y = vx dy = v'x + vx' subs that was pretty.

glewis15
 one year ago
Best ResponseYou've already chosen the best response.0it looks like you drew an ostrich
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.