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ExponentialOf(AngouriMath.Entity)

Method (no overloads)

Summary

e to the power of exponent, written without the exponential
where the exponent is a logarithm.

Remarks

This is not tidying, it is the difference between answering and not. The integrating
factor for y' + y/x = 1 is e^(int dx/x), which is e^ln(x). If that
stays an exponential of a logarithm, the second integral has no antiderivative for it
and the whole equation is declined. Measured, which is how it was found: every step but
that one came out.
Every arm here is load-bearing, and the general rule does not replace any of them.Simplify has folded e^ln(a) to a since
#1138, which is
what the paragraph above used to deny — but this method asks
InnerSimplified, and that pass does not carry the rewrite rules, so
e^ln(x) reaches it unfolded. Removing the whole method fails three
OrdinaryDifferentialEquationTest cases; removing only the e^ln(u) arm
fails two; and calling Simplify at the call site instead still fails one, because
nothing in the library folds e^(k ln u) to u^k — the shape an
antiderivative of k/x gives, and the reason the two Mulf arms exist.
Kept local rather than promoted to a rule for the same reason it was written local: the
scaled form e^(k ln u) = u^k is a principal-branch identity that reaches every
expression in the library and wants deciding on its own terms. Here the exponent was
built by this method and is known to be an antiderivative, which is what makes the
local reading sound without that argument.

AngouriMath

Table of contents

AngouriMath

ExponentialOf​(AngouriMath.​Entity)

ExponentialOf(AngouriMath.Entity)