wat r differential equations?

gabuds

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Jun 22, 2010
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i missed classes in univ so i lost this subject. i tried reading the book but couldnt understand.
one exercise:
determine the constant solution, if exist, that r the solution of the equattions below:
a) dx/dt=t(x-1)
 
gabuds said:
i missed classes in univ so i lost this subject. i tried reading the book but couldnt understand.
one exercise:
determine the constant solution, if exist, that r the solution of the equattions below:
a) dx/dt=t(x-1)

This separable variable ODE.

\(\displaystyle \frac{dx}{dt} \ \ = \ \ t\cdot (x-1)\)

What have you learnt about these types of equations. Your textbook must have some example problems.
 
uh i have no idea wat i have to do there
other exercises here: dx/dt = 1-x^2
dy/dx=y²+2y+1
dx/dt=x/t , t>0
 
gabuds said:
uh i have no idea wat i have to do there
other exercises here: dx/dt = 1-x^2
dy/dx=y²+2y+1
dx/dt=x/t , t>0

Did you understand the solutions of those three above?
 
gabuds said:
yee, like the derivate of a fuction x(t) equals to x/t for example

Can you show me - how that problem was solved?

Your original problem is very similar.
 
Subhotosh Khan said:
gabuds said:
yee, like the derivate of a fuction x(t) equals to x/t for example

Can you show me - how that problem was solved?

Your original problem is very similar.
oh i mean i dont know how its solved, i know wat it means
 
So then I'll solve that problem for you:

the derivative of a fuction x(t) equals to x/t for example

\(\displaystyle \frac{dx}{dt} \ \ = \ \ \frac{x}{t}\)

This is a separable variable problem - meaning the variables can be separated, grouped and isolated. In this case - it becomes:

\(\displaystyle \frac{dx}{x} \ \ = \ \ \frac{dt}{t}\)

We have all the parameters containing 'x' on one side - and all the parameters containig 't' on the otherside of the "=" sign. Next we integrate both sides

\(\displaystyle ln(|x|) \ \ = \ \ ln(|t|) + ln(C)\)

\(\displaystyle ln(|x|) \ \ = \ \ ln(C\cdot |t|)\)

\(\displaystyle |x| \ \ = \ \ C\cdot |t|\)

Problem solved - for your original problem follow the same steps.
 
gabuds said:
but wat do i do in this case?
dx/dt = 1-x^2

Same - put all the 'x's on one side and all the 't's on the otherside of the "=" sign
 
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