xartaan
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
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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.

hartnn
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try to isolate y

hartnn
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if ln a= b
then a=e^b

RyanL.
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when x=0 y=8
plug that solve for c and yeah isolate y

xartaan
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ok, so \[\ln(y)=\frac{ x }{ 5 }+C\] becomes \[y=e^(\frac{ x }{ 5 }+C)\]

xartaan
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so 8=e^(0+c), 8=e^c?

xartaan
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c=ln(8) ?

hartnn
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yup, c=ln 8
so
ln y +ln 8 = x/5
ln (y/8) = x/5
got this ?

hartnn
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property of log,
log Alog B =log (A/B)

xartaan
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ahhhh yes I see that

xartaan
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y=8*e^(x/5)

hartnn
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y=8*e^(x/5)

xartaan
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Haha yes, making every mistake posssible on this one. Thanks for the help!

hartnn
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welcome ^_^