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In the earlier section we introduced the Wronskian to assist us find out whether two solutions were a fundamental set of solutions. Under this section we will look at the other application of the Wronskian and also an alternate method of computing the Wronskian.
Let's begin with the application. We require introducing a couple of new concepts first.
Specified two non-zero functions f(x) and g(x) write down the subsequent equation
c f ( x ) + k g ( x ) = 0
See that c = 0 and k = 0 will make (1) true for all x regardless of the functions which we use.
Here, if we can get non-zero constants c and k for that (1) will also be true for all x so we call the two functions linearly dependent. Conversely, if the only two constants for that (1) is true are c = 0 and k = 0 so we call the functions linearly independent.
If there are (2n+1)terms in an AP ,prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n Ans: Let a, d be the I term & Cd of the AP. ∴ ak =
rectangles 7cm by 4cm
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Example: Find out a particular solution to y'' - 4y' - 12 y = 3e 5t Solution The point here is to get a particular solution, though the first thing that we're going to
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Calculus Calculus is a branch of mathematics which describes how one variable changes in relationship to another variable. It enables us to determine the rate of change of one
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
the segments shown could form a triangle
successful marketing research relies on accurate identification of the research objectives. Critically discuss when setting relevant research objectives, drawing on marketing theor
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