- #1

Yr11Kid

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

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- Thread starter Yr11Kid
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In summary, the conversation discusses a linear equation that requires an integrating factor to solve. The integrating factor is of the form exp(t) and can be used to simplify the equation by multiplying both sides. The result is an expression that can be easily integrated. The use of Sigma is either a constant or an infinite sum, and henlus' suggestion of using an integrating factor still applies.

- #1

Yr11Kid

- 8

- 0

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

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- #2

Eynstone

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

- #3

henlus

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- #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).

[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

henlus

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HallsofIvy said: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.

A general solution of a first order differential equation is a solution that satisfies the equation for all possible values of the independent variable. It contains one or more arbitrary constants that can take on different values to produce specific solutions.

To find the general solution of a first order differential equation, you must first separate the variables and then integrate both sides. This will result in an equation with one or more arbitrary constants. These constants can be determined by using initial conditions or boundary conditions.

A general solution is a solution that satisfies the equation for all possible values of the independent variable, while a particular solution is a specific solution that satisfies the equation for a given set of initial or boundary conditions. A general solution contains one or more arbitrary constants, while a particular solution does not.

No, a first order differential equation can only have one general solution. However, this general solution may contain multiple arbitrary constants that can take on different values to produce different particular solutions.

Yes, there are some first order differential equations that do not have a general solution. These equations are called non-integrable or non-elementary equations. In such cases, specific techniques or numerical methods must be used to find a solution.

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