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Differential Equations Lecture Work Solutions 52

Differential Equations Lecture Work Solutions 52 - To...

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To compute the coefficients, we need the integral L 0 cos 3 π L x sin L x dx Using the trigonometric identity sin a cos b = 1 2 (sin( a + b ) + sin( a b )) we have 1 2 L 0 sin ( n + 3) π L x + sin ( n 3) π L x dx Now for n = 3 the integral is 1 2 cos ( n +3) π L x ( n +3) π L | L 0 1 2 cos ( n 3) π L x ( n 3) π L | L 0 or when recalling that cos = ( 1) m L 2 π ( n + 3) ( 1) n +3 1 L 2 π ( n 3)
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