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I have the following equation:

$y=\frac{kv}{m\left(a-b\right)}\cdot\left(\frac{e^{-at}}{a^{2}}-\frac{e^{-bt}}{b^{2}}\right)$

$k$, $v$, $m$, $a$, and $b$ are all constants. t is time in seconds.

I would like to solve $t$ for a given $y$ value. ie. I would like to express the equation as:

$t = ...$

I tried Wolfram Alpha and Symbolab's equation solvers but they couldn't provide an answer. Is this a difficult one or practically impossible to solve?

mike
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    In a general manner, it is impossible. If $a$ and $b$ are in a ratio of $2,3,4$, it could reduce to a polynomial. – Claude Leibovici Jan 01 '20 at 09:42
  • Okay thanks. I'll just iterate through it with increasing time values until I get the y value I want and then record the time value that roughly provided it. – mike Jan 01 '20 at 10:05

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