Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

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

Psymon Group TitleBest ResponseYou've already chosen the best response.0
Checking answer? O.o
 one year ago

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

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

Psymon Group TitleBest ResponseYou've already chosen the best response.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.
 one year ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
'x=dx/dx=1
 one year ago

agentc0re Group TitleBest ResponseYou've already chosen the best response.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=(3x2y)dy%2B(x%2By5)dx%3D0&t=crmtb01
 one year ago

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

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

glewis15 Group TitleBest ResponseYou've already chosen the best response.0
it looks like you drew an ostrich
 one year ago
See more questions >>>
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.