Quick question about differential equations

[vande060]

Homework Statement

solve the equation

dy/dx = y/x

Homework Equations

The Attempt at a Solution

dy/dx = y/x

dy/y = dx/x

lny = lnx + c

my book gives the answer

y = kx

not sure how they got that, did they just take the log of the constant, because its just a constant and can be manipulated to simplify.

y = lnx + lnc

y = ln(xc)

k = c

y = kx ??

 

[SammyS]

Look at:

$$e^{\ln(y)}=e^{\ln(x)+C}$$

 

[vande060]

Look at:

$$e^{\ln(y)}=e^{\ln(x)+C}$$

would that be the same as saying

y = xe^c

 

[Mark44]

Yes. And e^c is just a constant, which you can call k.

 

[vande060]

Yes. And e^c is just a constant, which you can call k.

well that was easy thanks