I wish to solve an equation of the following type: $ ax+b = ce^{dx^2}$. I know about Lambert W function, however I do not see any way of solving the equation with $x^2$ instead of $x$. Is this possible?
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2I think it is unlikely, since Mathematica cannot solve even the case $x+1=e^{x^{2}}$. Of course, Mathematica is not perfect, and I am no expert. If $b=0$, however, then you can solve it by squaring both sides, solving the resulting equation for $x^2$, and discarding extraneous solutions. – MathIsFun7225 Feb 10 '21 at 17:38
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1Maybe useful https://math.stackexchange.com/questions/2309691/equations-solvable-by-lambert-function – cgiovanardi Feb 10 '21 at 19:10