I am stuck at this equation what method is appropriate and how I should solve it?
$$\left(x e^y-1\right)dy= -\left(e^{x+y}+e^y y\right)dx$$
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Welcome to MSE! Please use the basic tutorial and quick reference guide and review the Meta Read and enhance your question to provide your motivation/attempts. – Jessie Feb 12 '21 at 11:28
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What did you try? – beingmathematician Feb 12 '21 at 12:13
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If there is a solution, I bet that it would involve Lambert function. – Claude Leibovici Feb 12 '21 at 12:47
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There is a solution and it involves Lambert function. ! We are still waiting to know what you already tried. – Claude Leibovici Feb 12 '21 at 13:49