Recall that variation of parameters is used to solve second-order ODEs of the form
<em>y''(t)</em> + <em>p(t)</em> <em>y'(t)</em> + <em>q(t)</em> <em>y(t)</em> = <em>f(t)</em>
so the first thing you need to do is divide both sides of your equation by <em>t</em> :
<em>y''</em> + (2<em>t</em> - 1)/<em>t</em> <em>y'</em> - 2/<em>t</em> <em>y</em> = 7<em>t</em>
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You're looking for a solution of the form

where


and <em>W</em> denotes the Wronskian determinant.
Compute the Wronskian:

Then


The general solution to the ODE is

which simplifies somewhat to

Answer:
b = 36
Step-by-step explanation:
27 divided by 6 = 4.5
45 divided by 10 = 4.5
- so, each point was multiplied by 4.5
8 times 4.5 = 36
The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12
<h3>What is the simplified form of the expression</h3>
Given the expression;
5.5(x+6 1/2) - (x+9 1/3) - (19-x)
First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction
6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2
So, we have
(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )
Next, we remove the parentheses
11x/2 + 143/4 - x - 28/3 - 19 + x
11x/2 + 143/4 - 28/3 - 19
11x/2 + 317/12 - 19
11x/2 + 89/12
Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.
Learn more about fractions here: brainly.com/question/28039882
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