Dear scholars, I am working on the following equation and wonder whether my solution is correct. The actual problem is more complex but the example below captures the main features. I have not a lot of experience with the Lambert W function. Thanks in advance for your comments! Equation: $$Y=x \exp(x^2)$$ Substitute: $$u=x^2$$ Then: $$Y=\sqrt{u} \exp(u)$$ $$Y^2=u \exp(2u)$$ $$2Y^2=2u \exp(2u)$$ Then using W function: $$2u=W(2Y^2)$$ From which $$x$$ follows.