Simon Bridge said:Both pics are a bunch of hand-drawn equations and working out.
They are meaningless without the problem they belong to and the reasoning behind them, so I'll have to make some guesses in order to start helping you. In future, please try to describe the problem.
I can see a possible confusion in the line: $$k=\frac{1}{2k}\ln 3$$ ... have you used the same variable for two things here?
There is a red note: $$\frac{dy}{dx}+Py=a$$ ... if you didn't write that, then it may be a hint as to where you went wrong and you should look more closely at the DE you are trying to solve.
(I can't tell if that's supposed to be Py or Py)
$$ -v\frac{dv}{dk}=h+kv^2$$ ... is what you ended up with.
Assuming that is correct, it tidies up to:$$\frac{dv}{dk}+kv=-\frac{h}{v}$$
Which has form:$$\frac{dv}{dk}+p(k)v=q(v(k))$$... which you appear to have tried to solve via an integrating factor.
I'm guessing that this is what you want help with?
If so then: Compare with "Bernoulli's Equation".
If the writing in red is a hint, it appears to suggest that the initial DE is wrong... so the mistake is off the top of the page.
Simon Bridge said:OK - in general - do not use red pen on your own work.
If you have a DE of form ##y'+Py = Q## where P and Q are functions of x alone, then you can go right to an integrating factor.
But you don't have that form.
You have form: ##yy'+xy^2=c##: for c a given constant.
Look up how to solve Bernoulli's equation.
Simon Bridge said:OK - in general - do not use red pen on your own work.
If you have a DE of form ##y'+Py = Q## where P and Q are functions of x alone, then you can go right to an integrating factor.
But you don't have that form.
You have form: ##yy'+xy^2=c##: for c a given constant.
Look up how to solve Bernoulli's equation.
delsoo said:thanks for your reply! , i am still confused? would you mind to you show the full working here?
Simon Bridge said:First: Look up how to solve Bernoulli's equation.
If you won't take suggestions I cannot help you.
Simon Bridge said:First: Look up how to solve Bernoulli's equation.
If you won't take suggestions I cannot help you.
delsoo said:thanks for your reply! , i am still confused? would you mind to you show the full working here?
So no, we won't provide the full solution to your problem.On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.
... did you follow the suggestion?delsoo said:well, i stucked this part now... i can't get v=o which the bead stops
Bernoulli and Google is your friend here:delsoo said:sorry what do u mean by beroullli equation?
delsoo said:thanks for your reply! , i am still confused? would you mind to you show the full working here?
Ray Vickson said:o
Why are you asking a question? You are asking if you are still confused. If you are confused, just say so, but do not ask whether or not you are---that is what happens when you use a question mark. Now is a good time for you to break a bad habit.
Also: PF rules state specifically that we are not allowed to show you full workings.
delsoo said:how about partial working?
... so you didn't even bother to read the link in post #13: that has a partial working.how about partial working?
Simon Bridge said:... so you didn't even bother to read the link in post #13: that has a partial working.
Simon Bridge said:That looks like a different question.
How did you get on with this one?
A differential equation is a mathematical equation that describes how a quantity changes over time or space. It involves a function and its derivatives, and can be used to model a wide range of physical phenomena.
There are several types of differential equations, including ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve a single independent variable, while PDEs involve multiple independent variables. SDEs incorporate randomness or uncertainty into the equation.
Differential equations are used in a wide range of fields, including physics, engineering, economics, and biology. They can be used to model the behavior of systems over time, predict future outcomes, and optimize processes.
There are several techniques for solving differential equations, including separation of variables, substitution, and variation of parameters. Other methods include using power series, Laplace transforms, and numerical methods such as Euler's method or Runge-Kutta methods.
Initial conditions are values given at the starting point of a differential equation, while boundary conditions are values given at different points along the function's domain. These conditions are used to find the particular solution to a differential equation, as the general solution will have constants that can be determined using the initial and boundary conditions.