Answer:
G
Step-by-step explanation:
Answer:
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Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
4(2x + 1) - 3 = - 3(x - 4) ← distribute parenthesis on both sides
8x + 4 - 3 = - 3x + 12
8x + 1 = - 3x + 12 ( add 3x to both sides )
11x + 1 = 12 ( subtract 1 from both sides )
11x = 11 ( divide both sides by 11 )
x = 1
The differential equation
has characteristic equation
<em>r</em> ⁴ - <em>n </em>² <em>r</em> ² = <em>r</em> ² (<em>r</em> ² - <em>n </em>²) = <em>r</em> ² (<em>r</em> - <em>n</em>) (<em>r</em> + <em>n</em>) = 0
with roots <em>r</em> = 0 (multiplicity 2), <em>r</em> = -1, and <em>r</em> = 1, so the characteristic solution is
For the non-homogeneous equation, reduce the order by substituting <em>u(x)</em> = <em>y''(x)</em>, so that <em>u''(x)</em> is the 4th derivative of <em>y</em>, and
Solve for <em>u</em> by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by <em>u₁ </em>and <em>u₂</em>. Now we look for a particular solution of the form
where
where <em>W</em> (<em>u₁</em>, <em>u₂</em>) is the Wronskian of <em>u₁ </em>and <em>u₂</em>. We have
and so
So we have
and hence
Finally, integrate both sides twice to solve for <em>y</em> :