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sunloveBest ResponseYou've already chosen the best response.0
we cant chat here this is a question only zone
 2 years ago

sunloveBest ResponseYou've already chosen the best response.0
we will get in trouble if we do
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
@romeo.nkala Welcome to Open Study!!!! If you need to talk to someone use chat, don't post it here. This is for questions only Thanks:)
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
ow i apologise...i was taught to greet, before i ask questions
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
No worries, just ask questions:)
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
2(y+3)dxxydy=0 im asked to find differential equation
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
We have \[2(y+3)dx=xydy\] Let's bring x to one side and y to other we get \[2\frac{dx}{x}=\frac{y}{y+3} dy\] Now we'll integrate both sides \[\int 2\frac{dx}{x}=\int \frac{y+33}{y+3} dy\] \[\int 2\frac{dx}{x}= \int (1\frac{3}{y+3}) dy\] Now integrating we get \[2 \ln x+C= y 3 \ln {(y+3)}\] or \[y=2 \ln x3\ln (y+3) +C\] C= constant of integration
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
im doing this for the 1st time, i read through the note i cant seem to get the whole point and procedure. can you explain to me the important stuff
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Hey romeo, I was not here. What you don't understand?
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
the whole point of de
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Okay do you know differentiation and integration?
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Suppose we have \[ y=x^2\] Let's differentiate this we get \[\frac{dy}{dx}=2x\] so \[\frac{dy}{dx}2x=0\] This is a differential equation, it can also be written as \[dy2xdx=0 \] Here we started with y=x^2, that's why we know that the solution of the differential equation is y=x^2 Did you understand this?
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
yes that makes sense
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Here we had the solution from that we found the differential equation but it's not the case every time. We'll have the DE and we'd be required to find its solution.
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
In our question we are given \[2(y+3)dxxydy=0 \] We have to integrate this to find the solution or y If we have to solve a DE, we need it in this form \[f(y)dy=g(x) dx\] f is any function of y and g could be any function of x What we see that with dy we need a function of y and with dx we need a function of x. We'd not like function of y with dx or viceversa
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
wow ok.. so solving a de is solving for y?
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
or any other dependent variable
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
like u=5v u is dependent and v is independent
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
so do u always have to rearrange such that its in the form f(y)dy=g(x)dx?
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Yeah otherwise we can't integrate
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
can we try this one \[(x ^{2} xy+y ^{2})dxxydy=0\]
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
i cant seem to separate xy
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
It's a little complicated. There's no way it can be separated. it requires a different MO
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
MO or procedure. I'll explain you.
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
We have \[(x^2xy+y^2)dx=xy dy\] or \[xydy=(x^2xy+y^2) \] Let's divide both sides by xy, we get \[dy=(\frac{x}{y}1+\frac{y}{x})dx\] or \[\frac{dy}{dx}=\frac{x}{y}1+\frac{y}{x}\] Now we'll substitute \[v=\frac{y}{x}\] or \[y=vx\] Let's differentiate this we get \[\frac{dy}{dx}=v+x\frac{dv}{dx}\] Now substituting this in our DE, we get \[v+x\frac{dv}{dx}=\frac{1}{v}1+v\] Can you separate v and x now? V is the independent variable
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Yeah now we'll get \[x\frac{dv}{dx}=\frac{1v}{v}\] or \[\frac{v}{1v} dv=\frac{dx}{x}\] Now you integrate both sides to find v, in terms of x and then substitute v=y/x to get your final solution
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
DId you get it @romeo.nkala ?
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
yep got it. its the same
 2 years ago

ash2326Best ResponseYou've already chosen the best response.1
Yeah:D. This is just the basics of DE. You'll learn complex ones later:D
 2 years ago

romeo.nkalaBest ResponseYou've already chosen the best response.0
thanks alot!! by the way
 2 years ago
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