(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

solve dy/dx=e^(3x+2y) by separation of variables

3. The attempt at a solution

[itex]\frac{dy}{dx}=e^{3x+2y}[/itex]

[itex]\frac{dy}{dx}=e^{3x}e^{2y}[/itex]

[itex]e^{-2y}dy=e^{3x}dx[/itex]

[itex]\int e^{-2y}dy=\int e^{3x}dx[/itex]

[itex]e^{-2y}=-\frac{2}{3}e^3x + C[/itex]

[itex]-2y = ln(-\frac{2}{3}e^{3x}+C)[/itex]

[itex]y=1\frac{1}{2}ln(-\frac{2}{3}e^{3x}+C)[/itex]

Just a little wondering mostly about the natural log thing. Can I take the natural log of the -ve function wrt x because of the constant?

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# Homework Help: Solve dy/dx=e^(3x+2y) by separation of variables

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