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January 28, 2005, 05:25 
Differential eq.

#1 
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Would u be so kind to help a stupid student.How to solve the deff.eq.:
y(t)''+A*y(t)'B*sin(t)=0 Boundary codition you can envent yourself 

January 28, 2005, 06:45 
Re: Differential eq.

#2 
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(Book) Differential & Integral Calculus by Piskunov.


January 28, 2005, 07:03 
Re: Differential eq.

#3 
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Thanks,but I've got no possibility to take this book,I'm in Magdeburg,Germany,and there's no library in my company


January 28, 2005, 07:57 
Re: Differential eq.

#4 
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y(t) = C*exp(sqrt(A)*t) + D*exp(sqrt(A)*t)
+ B*sin(t)/(A1) of course if A<0 and A=/=1 C & D can be found using the initial conditions 

January 28, 2005, 08:23 
Re: Differential eq.

#5 
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thanks


January 28, 2005, 09:26 
Re: Differential eq.

#6 
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The solution is, give or take a slip in the algebra,
t = C + D.exp(At) + E.sin(t) + F.cos(t) where C & D are constants fixed by the initial condition and E= B/(1+A^2), F = AB/(1+A^2) 

January 28, 2005, 09:47 
Re: Differential eq.

#7 
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Ok thanks,at last everything is OK,but how to find C1,C2 out of initial conditions?I've forgoten


January 28, 2005, 09:51 
Re: Differential eq.

#8 
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for examople y(0)'=1,y''(0)=1


January 28, 2005, 09:57 
Re: Differential eq.

#9 
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You have, at t=0 values of y and y', write down the formulas for y and y' at t=0 and solve the equations. In your case D is determined trivially from the condition on y' substitute this into the condition for y to determine C.


January 28, 2005, 10:12 
Re: Differential eq.

#10 
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Thanks in advance,I got the disired.


January 28, 2005, 10:20 
Re: Differential eq.

#11 
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And how will be looking this eq. if I change it from the second order dif.eq. to a system of two eq. of first order?
dy(1)=y(2) dy(2)=A*y(2)+B*sin(t)??? 

January 28, 2005, 10:39 
Re: Differential eq.

#12 
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you're going to apply Runge Kutta methods , aren't you ?
so you set y=z' and if Y = [ y , z] is the vector solution, you have then the system Y'= [ z , z' ] or in other way z = y' z'= y'' = A*y + B sin(t) Am I right ? 

January 28, 2005, 11:01 
Re: Differential eq.

#13 
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I hope so,and what will happened with sin(t),should we take the derivative also,tha > cost???Am I right?


January 31, 2005, 04:59 
Re: Differential eq.

#14 
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well once you have Y' = F(Y,T) with F(Y,t) the vector function : F(Y,t)= [ y' ; A*y + B*sin(t)]
if you discretize with Euler method (for the sake of simplicity) : Y_n+1 = Y_n + Dt*F(Y_n,t) with initial values Y_0= [ y(t=0) ; z(t=0)=y'(t=0) ] So you needn't to calculate any more derivatives. hope I'm right 

January 31, 2005, 05:21 
Re: Differential eq.

#15 
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Thanks a lot for ur help!


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