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Here, let's take a look at sums of the fundamental components and/or products of the fundamental components. To do this we'll require the following fact.
Fact- Undetermined Coefficients
If YP1(t) is a particular solution for
y′′ + p (t) y′ + q (t ) y = g1 (t)
And if YP2(t) is an exact solution for
y′′ + p (t ) y′ + q (t) y = g2 (t)
So YP1(t)+ YP2(t) is an exact solution for
y′′ + p (t ) y′ + q (t ) y = g1 (t )+ g2(t)
This fact can be utilized to both find exact solutions to differential equations which have sums in then and to write down guess for functions which have sums in them.
Example of Imaginary Numbers: Example 1: Multiply √-2 and √-32 Solution: (√-2)( √-32) = (√2i)( √32i) =√64 (-1) =8 (-1) =-8 Example 2: Divid
5 years however, a man's age will be 3times his son's age and 5 years ago, he was 7 times as old as his son. Find their present ages.
a²+b²=1 a+b
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Reason for why limits not existing : In the previous section we saw two limits that did not. We saw that did not exist since the function did not settle down to a sing
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball , determine the number of blue balls in the bag.
Suppose the economy is now ‘open’ and thus has an external demand (e.g. from the government, exports, etc.) of the dollar amounts for each respective industry. In the latest budget
HOW MANY ZERO ARE THERE AT THE END OF 200
how to solve for x
Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
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