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xartaan
 2 years ago
Find the solution to the differential equation \[\frac{ dy }{ dx }+\frac{ y }{ 5 }=0 \]
with the initial condition y(0)=8
xartaan
 2 years ago
Find the solution to the differential equation \[\frac{ dy }{ dx }+\frac{ y }{ 5 }=0 \] with the initial condition y(0)=8

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xartaan
 2 years ago
Best ResponseYou've already chosen the best response.0So, ive done separation of variables, and integrated dy/(y) amd dx/5 and gotten ln(y) = x/5+C, but I am not sure what to do next.

RyanL.
 2 years ago
Best ResponseYou've already chosen the best response.0when x=0 y=8 plug that solve for c and yeah isolate y

xartaan
 2 years ago
Best ResponseYou've already chosen the best response.0ok, so \[\ln(y)=\frac{ x }{ 5 }+C\] becomes \[y=e^(\frac{ x }{ 5 }+C)\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1yup, c=ln 8 so ln y +ln 8 = x/5 ln (y/8) = x/5 got this ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1property of log, log Alog B =log (A/B)

xartaan
 2 years ago
Best ResponseYou've already chosen the best response.0Haha yes, making every mistake posssible on this one. Thanks for the help!
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