# General Solution of the first order differential equation

## Main Question or Discussion Point

dy/dt + y = Sigma Sin(nt)/n^2

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Multiply by exp(-(integral)Sigma Sin(nt)/n^2 dx) ) and integrate.

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.

HallsofIvy
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Is Sigma simply a constant of do you mean an infinite sum?
$$\frac{dy}{dt}+ y= \sum_{n=1}^\infty \frac{sin(nt)}{n^2}$$

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

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Is Sigma simply a constant of do you mean an infinite sum?
$$\frac{dy}{dt}+ y= \sum_{n=1}^\infty \frac{sin(nt)}{n^2}$$

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