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I'm working with a fairly complex equation and I need to carry out constrained optimization of the same. The first order differential equations are very messy to solve by hand and hence I thought to use online calculators. Problem with calculators like wolfram is that I cannot choose the variables with respect to which optimization needs to be done. If I use numbers in place of other variables it would defy the purpose. Are there any calculators available online for the problem I have? I am open to use coding based software like Matlab.

For example:
Maximize $\ ax^b−x $
w.r.t $\ x $
s.t. $\ x>0,a>1,0<b<1 $
The original problem is multivariable and much more complex. I don't want to optimize with specific values for a,b.

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You can set the decision variables in Wolfram Alpha. E.g.,

maximize [{x*q-q^2+a} , {q}]

maximizes the function $x*q-q^2+a$ w.r.t. the variable $q$.
For further details read the reference sheet of the Maximize function.

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You can use Mathematica to solve such problems.

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