Question

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Separation of Variables: Let v(t) be the velocity, in knots per hour, of a vessel at...

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?

Solutions

Expert Solution

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,
Keep posting questions.

milcah answered 1 year ago

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