(10 pts) (a) (2 pts) What is the difference between an ordinary differential equation and an initial value problem? (b) (2 pts)
1 answer:
Answer:
Step-by-step explanation:
(A) The difference between an ordinary differential equation and an initial value problem is that an initial value problem is a differential equation which has condition(s) for optimization, such as a given value of the function at some point in the domain.
(B) The difference between a particular solution and a general solution to an equation is that a particular solution is any specific figure that can satisfy the equation while a general solution is a statement that comprises all particular solutions of the equation.
(C) Example of a second order linear ODE:
M(t)Y"(t) + N(t)Y'(t) + O(t)Y(t) = K(t)
The equation will be homogeneous if K(t)=0 and heterogeneous if
Example of a second order nonlinear ODE:
(D) Example of a nonlinear fourth order ODE:
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Answer:
a)
b)
c)
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And is the probability of X happening.
(a) A fair die is rolled 50 times. X = number of times a 5 is rolled
The die is rolled 50 times, so .
Each roll can have 6 outcomes. So the probability that 5 is rolled is
(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.
You buy 16 boxes of cereal, so .
1 of 100 are winners. So .
(c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.
He plays 26 games, so .
He wins 25% of the time, so
We have that . So