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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.
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For complex number z, the minimum value of |z| + |z - cosa - i sina|+|z - 2(cosa + i sina )| is..? Solution) |z| + |z-(e^ia)| + |z-2(e^ia)| we see.....oigin , e^ia , 2e^ia , f
1/2+3/4
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