Solve the separable differential equation

[hardatwork]

Homework Statement

dx/dy=-0.6y
y(0)=5

Homework Equations

The Attempt at a Solution

I tried solving it by
$$\int$$dy/y=$$\int$$-0.6dx
ln(y)=-0.6x+c
ln(y(0))=-0.6(0)+c
ln(5)=c
ln(y)=-0.6x+ln(5)
y=$$e^{-0.6x}$$+5
But its incorrect. I don't know what I am doing wrong. Can someone helping see what I am doing wrong? Thank You so much!

 

[mbisCool]

You should solve for your function before substituting initial conditions. Remember that $$e^{ln|y|}=y$$

 

[gabbagabbahey]

Homework Statement

dx/dy=-0.6y

Is this a typo? Do really mean dx/dy=-0.6y, or do you mean dy/dx=-0.6y?

$$\int$$dy/y=$$\int$$-0.6dx
ln(y)=-0.6x+c
ln(y(0))=-0.6(0)+c
ln(5)=c
ln(y)=-0.6x+ln(5)
y=$$e^{-0.6x}$$+5
But its incorrect. I don't know what I am doing wrong. Can someone helping see what I am doing wrong? Thank You so much!

If $\ln y=-0.6x+\ln 5$, then

$$y=e^{-0.6x+\ln 5}=e^{\ln 5}e^{-0.6x}=5e^{-0.6x}\neq e^{-0.6x}+5$$

 

[hardatwork]

Okay. That makes so much sense. Thank You so much