I have the following to solve:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dx}{dt}=-\alpha xy;\quad y=y_0e^{-\beta t};\quad x(0)=x_0[/tex]

I separate variables and come up with:

[tex]\frac{dx}{x}=-\alpha y_0e^{-\beta t}dt[/tex]

[tex]\ln{x}=-\alpha y_0\int e^{-\beta t}dt=\frac{\alpha y_0}{\beta}e^{-\beta t}+C[/tex]

...so for a final answer I come up with:

[tex]x=x_0\exp{\left(\frac{\alpha y_0}{\beta}e^{-\beta t}\right)}[/tex]

..however the book says that the answer is:

[tex]x=x_0\exp{\left(\frac{-\alpha y_0\left(1-e^{-\beta t}\right)}{\beta}\right)}[/tex]

I cannot find where I went wrong, any ideas?

Thanks a lot.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Differential Equations Help

**Physics Forums | Science Articles, Homework Help, Discussion**