Question

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

Answer 1

cross multiply
\[\implies \frac{dx}x = 3t^2 dt\]
now integrate both sides

does that help?

Answer 2

or do you need more help?

Answer 3

i did that and got ln x = t^3 + C but the back of the book has it as x = Cexp(t^3). How did they get there?

Answer 4

\[\Large \ln x = t^3 + C\]
raise both sides by e
\[\Large \implies e^{\ln x} = e^{t^3 + C}\]
simplify...
\[\Large \implies x = e^{t^3 + C}\]
according to algebra...this is just
\[\Large \implies x = e^{t^3} \times e^C\]
constant raised to constant is just a constant
\[\Large x = e^{t^3} \times C\]
this is also written as
\[\Large \implies x = C\text{exp} (t^3)\]
did you follow that?

Answer 5

yes thank you for your help

Answer 6

welcome