# Math Help - dy/dx = -y/x

1. ## dy/dx = -y/x

Hello everybody,

I need to solve

dy/dx = -y/x

for some economics problem. Can anybody help me?

Thanks,

Rob

2. The DE you propose can be written as...

$\frac {dy}{y} = -\frac{dx}{x}$ (1)

Al thet you have to do is to integrate first and second term of (1) indicating the 'arbitrary constant' as $\ln c$...

Kind regards

$\chi$ $\sigma$

3. Originally Posted by robvaneijk
Hello everybody,

I need to solve

dy/dx = -y/x

for some economics problem. Can anybody help me?

Thanks,

Rob
$\frac{dy}{dx} = -\frac{y}{x}$

$\frac{1}{y}\,\frac{dy}{dx} = -\frac{1}{x}$

$\int{\frac{1}{y}\,\frac{dy}{dx}\,dx} = \int{-\frac{1}{x}\,dx}$

$\int{\frac{1}{y}\,dy} = -\int{\frac{1}{x}\,dx}$

$\ln{|y|} + C_1 = -\ln{|x|} + C_2$

$\ln{|y|} + \ln{|x|} = C$, where $C = C_2 - C_1$

$\ln{|y||x|} = C$

$\ln{|xy|} = C$

$|xy| = e^C$

$xy = \pm e^C$

$xy = A$ where $A = \pm e^C$

$y = \frac{A}{x}$.