In: Math
Separation of Variables:
Let v(t) be the velocity, in knots per hour, of a vessel at time
t, t = 0. After the second engine is turned on, its velocity
satisfies the differential equation ??/??=3?+22, with initial
condition v (0) = 2.
First use separation of variables to find an expression for v in
terms of t. Secondly, f the vessel cruising speed is 25 knots per
hour, how long will the vessel take to reach this speed?
PART(a):
The given DE is,
integrating on both sides,
where A is integration const,
put t = 0,
now the final solution becomes,
PART(b):
time is in hours.
I hope this answer helps,
Thanks,
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