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DEtools[symmetric_power] - calculate the symmetric power of a differential equation or operator
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Calling Sequence
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symmetric_power(L, m, domain)
symmetric_power(eqn, m, dvar)
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Parameters
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L
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differential operator
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m
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positive integer
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domain
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list containing two names
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eqn
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homogeneous linear differential equation
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dvar
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dependent variable
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Description
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If the argument domain is omitted then the differential specified by the environment variable _Envdiffopdomain is used. If this environment variable is not set then the argument domain may not be omitted.
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Instead of a differential operator, the input can also be a linear homogeneous differential equation having rational function coefficients. In this case the third argument must be the dependent variable.
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This function is part of the DEtools package, and so it can be used in the form symmetric_power(..) only after executing the command with(DEtools). However, it can always be accessed through the long form of the command by using DEtools[symmetric_power](..).
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Examples
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![_Envdiffopdomain := [Dx, x]](/support/helpjp/helpview.aspx?si=6491/file01383/math147.png)
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To illustrate formally the meaning of the output of this command, consider a general second order ODE
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The nth symmetric_power of ODE is another ODE having for a solution the nth power of the solution of ODE. For example, the solution of ODE can be written - formally - using the Maple DESol command; dsolve represents it that way:
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where in the above DESol(...) represents any linear combination of two independent solutions of ODE. The first symmetric power of ODE is then ODE itself (has for solution sol^1) and, for instance, for the second and third symmetric powers of ODE we have
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Download Help Document
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