find_the_fun
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Solve the DE by using separation of variables
[math]\frac{dy}{dx} = e^{3x+2y}[/math]
Break up [math]e^{3x+2y} = e^{3x}e^{2y}[/math] Move x's and y's to their own side of the equation.
[math]\frac{1}{e^{2y}} dy = e^{3x} dx[/math]
Integrate both sides of the equation to get [math]\frac{-e^{2y}}{2x}=\frac{e^{3x}}{3}+C[/math]
I don't know how to isolate the y; I don't know how to get it down from the exponent.
[math]\frac{dy}{dx} = e^{3x+2y}[/math]
Break up [math]e^{3x+2y} = e^{3x}e^{2y}[/math] Move x's and y's to their own side of the equation.
[math]\frac{1}{e^{2y}} dy = e^{3x} dx[/math]
Integrate both sides of the equation to get [math]\frac{-e^{2y}}{2x}=\frac{e^{3x}}{3}+C[/math]
I don't know how to isolate the y; I don't know how to get it down from the exponent.