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The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions.
Illustration: What is the actual solution to the subsequent IVP?
2ty' + 4y = 3; y(1) = -4
Solution: This is in fact easier to do than this might at first appear. From the earlier illustration we already identify that differential equations have all solutions are of the form:
y(t) = 3/4 + c/t2
All that we require to do is find out the value of c that will provide us the solution that we're after. To determine this all we require do is utilize our initial condition that are given as:
-4 = y(1) = 3/4 + c/12
c= -4 -3/4 = -19/4
Thus, the actual solution to the Initial Value Problem is:
y(t) = ¾ - 19/4t2
From this last illustration we can notice that once we have the general solution to a differential equation determining the actual solution is nothing more than applying the initial conditions and resolving for the constants which are in the general solution.
Liner Regression The calculations for our sample size n = 10 are described below. The linear regression model is y = a + bx Table: Distance x miles
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