x = a + b ecx
may be solved using the Lambert W functions:
xk = a - Wk(-bc eac) / c
where W(y) is a solution of: W(y) eW(y) = y .
If the argument of the W function is real and between -1/e and 0, then there are two real values: W0 (> -1) and W-1 (< -1).
If the argument is real and >=0, then there is one real value: W0.
In this example, x values are produced in a ramp source. Both sides of the equation are produced: y=x and z=a+becx. The result, r0=a-W0(-bceac)/c, is also determined and all three meet at the appropriate point:
This type of solver is coded into the "SolveExpTranscend" block under the "NumericalInversions" package. The use of this block on the far right reveals that there is a 2nd solution from W-1 at x~35.
.GNU_ScientificLibrary.Examples.specfunc.ExpTranscendEqs
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