A community for students.
Here's the question you clicked on:
 0 viewing
jms_zacher
 2 years ago
dy/dx = (y^2 + 2xy)/x^2
homogeneous diff equation
jms_zacher
 2 years ago
dy/dx = (y^2 + 2xy)/x^2 homogeneous diff equation

This Question is Open

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0well in such equations u can start with letting \[z=\frac{y}{x}\]

jms_zacher
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i figured all of that part out. Its after integrating using partial fractions is where im stuck

waleed_imtiaz
 2 years ago
Best ResponseYou've already chosen the best response.0... Seperate the variables integrate them

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.0ok so u have \[z+x\frac{dz}{dx}=\frac{z^2x^2+2zx^2}{x^2}=z^2+2z\]\[x\frac{dz}{dx}=z^2+z\]and finally\[\frac{dz}{z(z+1)}=\frac{dx}{x}\]i think this is where u were stuck so just note that\[\frac{1}{z(z+1)}=\frac{1}{z}\frac{1}{z+1}\]makes sense?
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.