How would I go about solving this? I don't necessarily need to express y as a function of x but the general solution would be accepted.
I understand it's a homogenous equation, I was able to split it up into two separate integrals but I can't see a clear method of integration without it getting really messy.
>>7879177
their just like fractions you move them around and get xdx= (x+y)dy and you integrate those
>>7879177
Separation of variables
>>7879177
do the division
x/x+y, x cancels out. d/dx = y
The answer is x - ln(x+y) + C
Looks very hard.
Dimensional analysis suggests a particular solution y(x)=c·x, which indeed works out, but the general solution will be something silly.
>>7879177
sub in z=y/x giving dy/dx=z+x dz/dx
after that you can separate and integrate
>>7879236
to piss you off
[eqn]y'=\frac{x}{x+y}\Leftrightarrow xy'+yy'=x \Leftrightarrow (xy)'+(y-1)y'=(\frac{1}{2}x^2)' \Leftrightarrow (xy+\frac{1}{2}(y-1)^2)'=(\frac{1}{2}x^2)' [/eqn]
>>7879248
>lel i wuz just pretending 2 b retard Xdd
Sure thing, kid. Hope Calc I is going well for you.
>>7879279
I'm in Calc II actually.
>>7879832
Literally Mt. Stupid.
>>7879177
Simple answer, just do it numerically, python has great tools for that. Also solving things numerically is a lot easier
>>7880121
>lel im a stronk independent cs major who don't need no 2hard4me math classes
>>7879271
umm... isn't this the answer?
>>7880936
no shit, half the people in this thread are fucking retarded in case you didn't notice
oh wait i misread your post
>>7880936
of course that's not the fucking answer you fucking retard that's not even a fucking solution to a differential equation
>>7879279
t. anon asking /sci/ for homework help
In my de class, we would multiply both sides by the denominator and dx and work from there.
I might be hijacking the thread, but what does it mean when we multiply by the differential dx? What are we actually doing at that point? It seems handwavey to me.
>>7879177
>How would I go about solving this?
Some algebra and introduce an integrating factor to get it into an exact differential form and you're home free
mF(x,y)dy + mF(x,y)dx = 0
m is integrating factor
Is it legal to just cross multiply the fraction so I have x=y'(x+y) and rearrange it so I have x-xy'=y'y and integrate both sides?
>>7880992
It means you do (d/dx), cancel out the d because division stuff. (x), now run the equation as normal.
>>7880975
Oh come on... do you even math? He's got it in the form g' = f'. The final step g=f+const is less than trivial.
>>7881824
[math]y'=\frac{x}{x+y}[/math]
[math]xy'+yy'=x[/math]
[math](xy)'+(y-1)y'=(\frac{1}{2}x^2)'[/math]
[math](xy+\frac{1}{2}(y-1)^2)'=(\frac{1}{2}x^2)'[/math]
[math]xy+\frac{1}{2}(y-1)^2=\frac{1}{2}x^2 + C[/math]
>>7881084
what the fuck.
honest question:
would anyone manage to solve this without wolfram alpha?
>>7883082
It's a common trick, but hard to see if you're not really used to looking for tricks.
dy/dx = 1/(1+y/x) you can sort of see that dy/dx and y/x are similar. So you can do the substitution y/x=u, then differentiate this and pray it works out, which it does as you can see.
>>7883082
yes, it is from a well known class of ODE called homogeneous differential equations
their solution is well known and should be covered in any intro diffy q course
>>7879859
>tfw feel like I'm past mount stupid
>tfw in "science writing" course (required english class)
>tfw forced to write essays about topics that I only understand at my babby's first undergrad level
feels bad man
can't wait for grad school where i'll be forced to pretend to know what the fuck i'm talking about every day to people who know well enough that I don't know anything
>>7883082
>trivial computational problems
>impossible to solve by hand
Nigga if an ODE has a well-posed analytic solution, it's already been solved, thoroughly studied, and fully documented -- probably since the 19th or 20th century. Go see at what modern work in ODEs and PDEs looks like and you'll realize that questions like OP's are beyond trivial.
>>7883206
Yeah, I agree with this. Closed form solutions are cute, but they're literally just jerking off and a waste of time.
>>7879832
You don't learn that till calc 4.
Holy fuck 30+ replies on a baby's first homogeneous ODE homework problem with 99% of the replies literally just making stuff up
Fuck /sci/ this place is garbage
>>7883235
:^)
>>7883218
Really? My uni didn't teach us how to solve these problems until at least calc 7
>>7883218
False. I'm in Calc II, we learned these in late Calc I.
>>7883332
Which solution is yours
>>7883206
so what you are saying is that you find it easy because others already did all the work and studied it and basically did all the work for you.
good job you suck
>>7883082
protip: 90% of all the ODE's/PDE's out there are solved numerically.
>>7879177
Why am I getting a solution of the form phi*x, where phi is the golden ratio conjugate? I mean, it clearly works out when I do the substitution, but it doesn't seem to show up on any of your solutions so I might be doing something wrong.
>>7883235
>30+ replies
>99% of the replies
Lrn2diophantus
Differentiate one variable, while keeping the other one as a constant. Then differentiate the other variable while keeping the first one as a constant. Remember the rules for differentiating fractals
>>7879189
gr8b8m8
>>7884297
That's pretty cool. How did you arrive at that?
>>7879177
shit, I haven't done this stuff for so long I can't even remember the general approach
now I am intrigued. gonna try and solve this shit now
>>7880121
Fuck off
>>7883224
It checks.
>>7884587
thanks anon-desu
>>7879177
Quotient rule?
>>7885883
Maybe with whatever kind of retard math you're using.
>>7883274
>calc 7
hahaha. You must be burgerstani because I am le smelly yuropeen and saw it in calc 5.3333333333
I'm so superiorer then you, senpai. Go clap now, kek m8 senpai
I am doing calc 12 currently and am confused by the notation of d/dx, dy/dx and d^2y/dx^2. Sometimes the book uses that or it uses prime so f(x) becomes f'(x) which is the derivative. When am I supposed to use one or the other? I'm going through a self taught course so I have no feedback from a teacher. Example
>y= x^2-2x+5
Sometimes the derivative is noted as d/dx and sometimes it is noted as y'
any ideas?
>>7886081
d/dx means to take the derivative with respect to x. dy/dx is the derivative of y with respect to x.
y' is the derivative of y with respect to whatever the independent variable is.
They are two different notations for basically the same thing. However though, I never see df/dx, always f'(x). I usually see y' in differential equations, just because of how often derivations appear and you don't want to write dy/dx so many times until you get tired of it.
>>7883082
I managed to solve it without wolfram. It's not that hard anon, just a matter of knowing what method to use, after that it's just heavy algebra and integration.
