Nandan_78
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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.
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.