Question

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

Answer 1

integral?

Answer 2

Differentiate..lol

Answer 3

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

Answer 4

i got it to ln(x)= t^3 +C

Answer 5

\[\frac{\text dx}{\text dt}=3xt^2\]
\[\frac{\text dx}{x}=3t^2\text dt\]
\[\int\frac{\text dx}{x}=\int3t^2\text dt\]
\[\ln x=t^3+c\]

Answer 6

how to i get from this to x=Ce^(t^3)

Answer 7

\[\ln x=t^3+c\]\[e^{\ln x}=e^{t^3+c}\]\[x=e^ce^{t^3}\]\[x=ke^{t^3}\]

Answer 8

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
\[\Large x=Ce^{t^3}\]

Answer 9

thanks