Find y = f(x) passing through (0, 6) with dy/dx = y - 2

[paulxzt]

Find the function y=f(x) that passes through the point (0,6) that has dy/dx = y - 2

Im kinda having trouble with integrating the slope..

How do i go about when there is y on the dx side if i take dx to the other side

dy = (y-2)dx

do i do dy/(y-2) = dx ?

thanks for any help

 

[skeeter]

what you just did is called separation of variables ...

dy/(y-2) = dx

integrate both sides ...

ln|y-2| = x + C₁

change to an exponential equation ...

y = 2 + C₂e^x

last step ... use your initial condition to find C₂ and you're done.

 

[paulxzt]

what you just did is called separation of variables ...

dy/(y-2) = dx

integrate both sides ...

ln|y-2| = x + C₁

change to an exponential equation ...

y = 2 + C₂e^x

last step ... use your initial condition to find C₂ and you're done.

OH omg im so stupid.. I kept thinking that it had to be in dy/y form to be ln|y|.. grr thanks!