General Solution of the first order differential equation

  • Thread starter Yr11Kid
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  • #1
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dy/dt + y = Sigma Sin(nt)/n^2
 

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  • #2
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Multiply by exp(-(integral)Sigma Sin(nt)/n^2 dx) ) and integrate.
 
  • #3
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I think that this is a linear equation that requires an integrating factor of the form: exp(1)dt. Multiply both side of the equation by this factor. The LHS reduce to d(y.exp(t))/dt. You can then integrate both side.
 
  • #4
HallsofIvy
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Is Sigma simply a constant of do you mean an infinite sum?
[tex]\frac{dy}{dt}+ y= \sum_{n=1}^\infty \frac{sin(nt)}{n^2}[/tex]

In any case henlus' suggestion works- although he meant "integrating factor of the form exp(t)", not exp(1).
 
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  • #5
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Is Sigma simply a constant of do you mean an infinite sum?
[tex]\frac{dy}{dt}+ y= \sum_{n=1}^\infty \frac{sin(nt)}{n^2}[/tex]

In any case henlus' suggestion works- although he meant "integrating factor of the fore exp(t)", not exp(1).
You're right.
 

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