A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Solve the initial value problem:
x(dy/dx)+y(x) = 9y(x)^(2), y(1) = 1
anonymous
 3 years ago
Solve the initial value problem: x(dy/dx)+y(x) = 9y(x)^(2), y(1) = 1

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[x \frac{ dy }{dx } + y(x) = 9y(x)^2 , y(1) =1\] Just the equation a little neater

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I would solve for dy/dx and intergrate.

UnkleRhaukus
 3 years ago
Best ResponseYou've already chosen the best response.0the ex's int he brackets are just indicating the independent variable right?\[x \frac{ \text dy }{\text dx } + y = 9y^2 , \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and we know y(1) = 1.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I believe so, that's just how its been written. I'll try solving for dy/dx and integrating then,

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So I would sub those in.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2u realize that you can separate the variables easily here ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ dy }{ dx } = \frac{ 9y(x)^2y }{ x }\] Not too familiar with these problems, but basically i need to integrate that, no?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2u bring all terms of one variable on one side of = sign, like this : \(\large \frac{1}{9y^2y}dy=\frac{1}{x}dx\) then integrate

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2can u integrate both sides now ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0think i got it, left an x over the y side so i confused my self. \[1 = \ln(19y)\ln(y)\]

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2u integrated yvariable correctly , but what about \(\int (1/x)dx\) its not =1

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2i meant u should get something like this : \(\ln x=ln(19y)lny+c\) then use logarithmic properties to simplify

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Okay, catching on think i figured out what i did wrong when i integrated last anyway.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe y = \[\frac{ 1 }{ x+9 }\] May be a final solution, just simplifying the equation?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2ln cx= ln (19y)/y cxy= (19y) now use y(1) = 1 to find c.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2u got this simplification ? >ln cx= ln (19y)/y

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yup, \[C(1)(1)=19(1)\] \[C=10\] \[C=10\] \[10xy=(19y)\]

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.210xy =19y or 10xy9y+1=0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ahh, forgot the negative, think i have enough to try a few more of these questions any way. Thank you. :)
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.