Bernoullis' Equation is given by: (1) where . Solve this Bernoulli equation:
NOTE: You may want to use the substitution which will reduce any nonlinear equation of the form above in (1), where and
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So this looks like an integrating factor problem, but I get stuck when doing it. And the substitution thing gets confusing.
you should have caught yourself by doing it again. to get rid of the in front, you multiplied through by -2, correct? what is ?
EDIT: Ok, you caught yourself, good job. well, it wasn't a waste of time. you'll be more careful with such things from now on, and it will save you time in the future. we tend to make less mistakes if it hurts to make them
Alright, Jhevon. How does this look?
Integrating factor, M(t) is:
Multiply each term by M(t)
Use product rule in reverse:
Take integral
Subt. back in for u
Solve for y:
Thus,
QUESTION ON THIS LAST PART: is it y = +\- sqrt(...) or do we not have to worry about the negative.
Thanks
yes, we need the +/- here. we have no basis on which to choose the positive over the negative. if we were given initial conditions or some other conditions to fulfill that would cause a negative or a positive answer to be impossible, then we would drop one of the signs