- #1

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dy/dt + y =[tex]\infty[/tex][tex]\sum[/tex]n=1Sin(nt)/n^2

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- Thread starter Yr11Kid
- Start date

- #1

- 8

- 0

dy/dt + y =[tex]\infty[/tex][tex]\sum[/tex]n=1Sin(nt)/n^2

Last edited:

- #2

- 17

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[tex]

\frac{\mathrm{d}y}{\mathrm{d}t} = P(t)y(t) + Q(t)

[/tex]

with

[tex]P(t)\equiv -1[/tex] and [tex]Q(t):=\sum_{n\ge 1}{\frac{\sin(nt)}{n^2}}[/tex]. So, try with the formula

[tex]

y(t) = \exp\left(\int{P(t)\mathrm{d}t}\right)\left(\int{Q(s)\exp\left(-\int{P(s)}\mathrm{d}s\right)\mathrm{d}s})\right) \biggr|_{s=t}

[/tex]

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