What is the measure of angle ACB
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Answer:
<em>The particular integral of given differential equation</em>
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<em> General solution of given differential equation</em>
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Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given Differential equation y'' − 5 y' + 4 y = x
Given equation in operator form
D²y - 5 Dy + 4 y = x
⇒ ( D² - 5 D + 4 ) y =x
⇒ f(D) y = Q
where f(D) = D² - 5 D + 4 and Q(x) = x
<em>The auxiliary equation f(m) =0</em>
<em> m²-5 m + 4 =0</em>
m² - 4 m - m + 4 =0
m ( m -4 ) -1 ( m-4) =0
(m - 1) =0 and ( m-4) =0
<em> m = 1 and m =4</em>
<em>The complementary function </em>
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<u><em>Step(ii)</em></u>:-
<u><em>particular integral</em></u>
<em>Particular integral</em>
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<em>taking common '4' </em>
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<em>applying binomial expression</em>
<em> ( 1 + x )⁻¹ = 1 - x + x² - x³ +..... </em>
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<em>Now simplifying and we will use notation D = </em><em></em>
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<em>Higher degree terms are neglected</em>
<em> </em><em></em>
<em>The particular integral of given differential equation</em>
<em> </em><em></em>
<u><em>Final answer</em></u><em>:-</em>
<em> General solution of given differential equation</em>
<em> </em><em></em>
<em> </em><em></em>
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