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differential equations

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f(x) + f ''''(x)=0 2013-03-05
From Andreea:
Hei. I donít speak lot of english but here is my question,hope u understand: f(x) + f ````(x)=0. so, my question. what is f(x), where f ````(x) is f(x) derivative by four time ? i tried to find the answer and i knew f(x) is something like that f(x)=e^x*sinx but miss something.
Answered by Brennan Yaremko.
Separating variables 2008-11-04
From Terry:
by separating variables solve the initial value problem

(x+1)y' + y = 0 y(0) = 1

Answered by Harley Weston.
The integrating factor method 2004-08-05
From A student:
Whilst using the integrating factor method, I am required to integrate a function multipled by another function.

say f(t) = exp(kt) and some other function g(t); where exp = exponential and k is some constant.

Integral f(t)*g(t) dt or Integral exp(kt)*g(t) dt

What would the result of this integral be? I have never met an integral like this before. Would it simply be exp(kt)*g(t)/k? More specifically, the problem and my attempted answer is in PDF format:

In my attempted solution, I am unsure about the last two lines I have written out, as it relates to integrating a function multipled by another function.

Answered by Harley Weston.
Undetermined coefficients 2001-11-22
From Hoda:
The equation is:

y" - 2y' + y = t et + 4

We need to use The method of Undetermined coefficients. I have tried assuming that the solution is Atet+Bet+C, but all I get is C=4 and I tried (At2+Bt+C)et+D, but again I get 0=0 when I calculate the first and second derivatives, so i get no information on the constants. Any suggestions?


Answered by Harley Weston.
A mixture problem 2000-03-06
From Rebecca Edwards:
A tank in which cholocate milk is being mixed contains a mixture of 460 liters of milk and 40 liters of chocolate syrup initially. Syrup and milk are then added to the tank at the rate of 2 liters per minute of syrup and 8 liters of milk per minute. Simultaneously the mixture is withdrawn at the rate of 10 liters per minute. Find the function giving the amount of syrup in the tank at time t.
Answered by Harley Weston.
 
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