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anonymous
 4 years ago
Both y = 2e^t and y = e^t are solutions of the differential equation dy/dt = y. Since
this equation is autonomous the graph of y=2e^t can be obtained from the graph of
y=e^t by horizontal translation. By how much does one have to translate the graph
of y=e^t horizontally to obtain the graph of y=2e^t?
Does this question make sense?
anonymous
 4 years ago
Both y = 2e^t and y = e^t are solutions of the differential equation dy/dt = y. Since this equation is autonomous the graph of y=2e^t can be obtained from the graph of y=e^t by horizontal translation. By how much does one have to translate the graph of y=e^t horizontally to obtain the graph of y=2e^t? Does this question make sense?

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2I'm thinking ln2\[\large e^{t+\ln2}=2e^t\]...makes sense to me at least :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so what would the horizontal translation be?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2ln2 units to the left

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2we are changing\[f(t)\to f(t+\ln2)\]which is a translation of ln2 units left

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0do you know what the answer to this is? Find the general solution to (b) dy/dt = t^2y^3 i think i have the right answer but want to be sure.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i got \[y=\pm \sqrt{3/2t^3 + c}\]

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2I think you lost a minus sign, no?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0theres a very good chance .. what should the asnwer look like?

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2\[\int\frac{dy}{y^3}=\int t^2dt\]\[\frac1{2y^2}=\frac{t^3}3+C\to\frac3{2t^3+C}=y^2\]\[y=\pm\sqrt{\frac3{2t^3+C}}\]which would change the domain
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