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Norwin Dole's question at Yahoo! Answers about a differential equation

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661

Fernando Revilla

Well-known member
MHB Math Helper
Jan 29, 2012
661
We can solve it by separation of variables:

[tex]\dfrac{dy}{y}=\dfrac{e^{2x}\;dx}{4+e^{2x}}[/tex]

Integrating both sides:

[tex]\ln |y|=\dfrac{1}{2}\ln|4+e^{2x}|+C=\ln \sqrt{4+e^{2x}}+C[/tex]

Equivalently,

[tex]y=C_1\left(\sqrt{4+e^{2x}}\right)[/tex].