First-order differential equations by seperating variables..

[hank]

Ok, here's my problem:

dy/dt = -y/(50+t)

Here's my attempt:

y/dt = -dt/(50+t)

ln|y| + C = -ln|t+50| - C //Stuck here, not sure if distribution of minus is correct.
y + e^C = ?? //Stuck here too, not sure how to "e" the right side.

 

[galactus]

You separated correctly. Upon integrating you get:

\(\displaystyle \L\\ln(y)=-ln(50+t)+C\)

e to both sides:

\(\displaystyle \L\\y=e^{-ln(50+t)+C}\)

\(\displaystyle \L\\y=e^{-ln(50+t)}e^{C}\)

You can let \(\displaystyle e^{C}=C_{1}\) because it is a constant also.

\(\displaystyle \L\\y=\frac{C_{1}}{t+50}\)

 

[hank]

Makes sense.

TYVM!