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romeo.nkala
 3 years ago
hello guys
romeo.nkala
 3 years ago
hello guys

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

sunlove
 3 years ago
Best ResponseYou've already chosen the best response.0we will get in trouble if we do

ash2326
 3 years ago
Best 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:)

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

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1No worries, just ask questions:)

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.02(y+3)dxxydy=0 im asked to find differential equation

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1We 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

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.0im 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

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Hey romeo, I was not here. What you don't understand?

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.0the whole point of de

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Okay do you know differentiation and integration?

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Suppose 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?

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.0yes that makes sense

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Here 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.

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1In 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

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

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1or any other dependent variable

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1like u=5v u is dependent and v is independent

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

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Yeah otherwise we can't integrate

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

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.0i cant seem to separate xy

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1It's a little complicated. There's no way it can be separated. it requires a different MO

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1MO or procedure. I'll explain you.

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1We 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

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Yeah 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

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1DId you get it @romeo.nkala ?

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.0yep got it. its the same

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.1Yeah:D. This is just the basics of DE. You'll learn complex ones later:D

romeo.nkala
 3 years ago
Best ResponseYou've already chosen the best response.0thanks alot!! by the way
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