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

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xartaan Group TitleBest ResponseYou've already chosen the best response.0
So, 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.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
try to isolate y
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
if ln a= b then a=e^b
 one year ago

RyanL. Group TitleBest ResponseYou've already chosen the best response.0
when x=0 y=8 plug that solve for c and yeah isolate y
 one year ago

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

xartaan Group TitleBest ResponseYou've already chosen the best response.0
so 8=e^(0+c), 8=e^c?
 one year ago

xartaan Group TitleBest ResponseYou've already chosen the best response.0
c=ln(8) ?
 one year ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
property of log, log Alog B =log (A/B)
 one year ago

xartaan Group TitleBest ResponseYou've already chosen the best response.0
ahhhh yes I see that
 one year ago

xartaan Group TitleBest ResponseYou've already chosen the best response.0
y=8*e^(x/5)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
y=8*e^(x/5)
 one year ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.1
welcome ^_^
 one year ago
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