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I know we can solve e^x=x by the Lambert W function, but is it possible to solve the following equation:
a*(e^(2x)-e^x)+b*x=c
in terms of a, b, and c.
a*(e^(2x)-e^x)+b*x=c
in terms of a, b, and c.
Solving for x given a,b,c you mean? That would be the intersection of a line with a quadratic in e^x... that is $$ e^{x}\left ( e^x - 1\right ) = mx+k$$ ...where ##m=-b/a## and ##k=c/a##.solve: a*(e^(2x)-e^x)+b*x=c ... in terms of a, b, and c.
Welcome to PF;
Solving for x given a,b,c you mean? That would be the intersection of a line with a quadratic in e^x... that is $$ e^{x}\left ( e^x - 1\right ) = mx+k$$ ...where ##m=-b/a## and ##k=c/a##.
And you want to find x given m and k.
That help?