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haganmc

  • 2 years ago

solve the seperable equation: dx/dt=3xt^2

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  1. alexwee123
    • 2 years ago
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    integral?

  2. Yahoo!
    • 2 years ago
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    Differentiate..lol

  3. saadi
    • 2 years ago
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    separate the variables (1/x)dx=3t^2dt integrate both sides can you do this ?

  4. haganmc
    • 2 years ago
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    i got it to ln(x)= t^3 +C

  5. UnkleRhaukus
    • 2 years ago
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    \[\frac{\text dx}{\text dt}=3xt^2\] \[\frac{\text dx}{x}=3t^2\text dt\] \[\int\frac{\text dx}{x}=\int3t^2\text dt\] \[\ln x=t^3+c\]

  6. haganmc
    • 2 years ago
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    how to i get from this to x=Ce^(t^3)

  7. UnkleRhaukus
    • 2 years ago
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    \[\ln x=t^3+c\]\[e^{\ln x}=e^{t^3+c}\]\[x=e^ce^{t^3}\]\[x=ke^{t^3}\]

  8. saadi
    • 2 years ago
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    ok 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 \[\Large x=Ce^{t^3}\]

  9. haganmc
    • 2 years ago
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    thanks

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