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anonymous
 4 years ago
does the IVP dy/dt=y*t^(1/2), y(1)=1 have a unique solution on an interval containing t=1?
anonymous
 4 years ago
does the IVP dy/dt=y*t^(1/2), y(1)=1 have a unique solution on an interval containing t=1?

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1looks seperable to me

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[lny =\frac{2}{3}t^{3/2}+C \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0IVP=initial value problem. i have y=e^(2/3t^(3/2))+1e^(2/3) but it should be y=e^(2/3(t^(3/2)1))...not the same

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[\large y =exp(\frac{2}{3}t^{3/2}+C)\] \[y =exp(\frac{2}{3}t^{3/2})*exp(C)\] \[y =C_1\ exp(\frac{2}{3}t^{3/2})\] \[1 =C_1\ exp(\frac{2}{3})\] \[exp(\frac23) =C_1\] if i see it right

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you say seperable meaning not unique? cuz it should be unique...

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1seperable meaning its easy to see if theres a solution :)

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.2The solution is unique within an interval if the function y and its derivative are continuous on the interval.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[\frac{dy}{dx}=f(x)\ h(y)\] \[\frac{1}{h(y)}dy=f(x)dx\] \[\int(\frac{1}{h(y)}dy=f(x)dx)\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i see where i messed up. but why do you have 2/3?^^^

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1divide off the e^{2/3}

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1division makes an exponent go negative

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0same question...\[dy/dt=6y ^{2/3}\] y(1)=0. i'm not getting 0 so i need verification. i got \[y=(2tC)^{3}\] C=8/19...
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