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March 12th, 2011, 06:11 AM   #11
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Re: Linear differential equations

x = 1/sec(t) + c
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March 12th, 2011, 07:21 AM   #12
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Re: Linear differential equations





You need to multiply both t and C by cos(t) = 1/sec(t).
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March 12th, 2011, 11:33 AM   #13
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Re: Linear differential equations

Oh i see, i made the mistake on integrating swopping from one sin to another, more practice on these sort of equations is needed I think

I have a tricky question to solve, well it seems it.

The temperature T(measured in degrees) of a body immersed in an atmosphere of varying temperature is given by :

dT/dt + 0.1T = 5 - 2.5t , find the formula for the temperature at time t if T=60degrees when t=0

Would the use of the usual method be suitable for solving this problem, and given the boundaries would allow me to evaluate at the end if the solution is worked correctly.
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March 12th, 2011, 11:40 AM   #14
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Re: Linear differential equations

Yes, your equation is already given in standard linear form, so compute your integrating factor, then integrate to get the general solution (you'll have to use integration by parts on the right-hand side), then use your initial conditions to find the particular solution.

I got:



If you did not get something equivalent, post your work, and we'll figure out where the error is.
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March 12th, 2011, 01:06 PM   #15
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Re: Linear differential equations

right, im not confident with this one at all but heres my shot at it .

obtain integrating factor = e^0.1t

multiply std form equation by integrating factor
e^0.1t dT/dt e^-(0.1t) T = ^0.1t (5-2.5t)

d/dt T/e^0.1t = e^0.1t (5-2.5t)

integrate wrt t

T/e^0.1t = e^0.1t (300-25t) + C

T=e^0.1t (300+25t)+Ce^0.1t
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March 12th, 2011, 02:05 PM   #16
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Re: Linear differential equations

You obtained the right integrating factor, but from there it went south!

Multiplying the equation in standard form by the integrating factor gives:









Use integration by parts on remaining integral, where:



giving:

thus we have:







thus

giving:

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March 13th, 2011, 12:11 AM   #17
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Re: Linear differential equations

I tried, but thank you for going over that. Going to study that today to make sure it goes in
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