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anonymous
 4 years ago
solve the seperable equation:
dx/dt=3xt^2
anonymous
 4 years ago
solve the seperable equation: dx/dt=3xt^2

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0separate the variables (1/x)dx=3t^2dt integrate both sides can you do this ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i got it to ln(x)= t^3 +C

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1\[\frac{\text dx}{\text dt}=3xt^2\] \[\frac{\text dx}{x}=3t^2\text dt\] \[\int\frac{\text dx}{x}=\int3t^2\text dt\] \[\ln x=t^3+c\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0how to i get from this to x=Ce^(t^3)

UnkleRhaukus
 4 years ago
Best ResponseYou've already chosen the best response.1\[\ln x=t^3+c\]\[e^{\ln x}=e^{t^3+c}\]\[x=e^ce^{t^3}\]\[x=ke^{t^3}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok now you can write in explicit form raise both sides to e power \[\Large e^{\ln(x)}=e^{t^3+C}\] \[\Large x=e^ce^{t^3}\] or \[\Large x=Ce^{t^3}\]
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