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Unformatted text preview: 1 4. If an equation P ( t ) y 00 + Q ( t ) y + R ( t ) y = 0 is not exact, one can look for an integrating factor μ ( t ) such that μ ( t ) P ( t ) y 00 + μ ( t ) Q ( t ) y + μ ( t ) R ( t ) y = 0 is exact. • Show that such a factor μ ( t ) should satisfy the adjoint equation Pμ 00 + (2 PQ ) μ + ( P 00Q + R ) μ = 0 to ensure that the equation μ ( t ) P ( t ) y 00 + μ ( t ) Q ( t ) y + μ ( t ) R ( t ) y = 0 is exact. • Show that the adjoint equation of the adjoint equation is the original equation Py 00 + Qy + Ry = 0. • Compute the adjoint equation of the Airy equation y 00ty = 0 and of the Bessel equation t 2 y 00 + ty + ( t 2ν 2 ) y = 0. 2...
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This note was uploaded on 11/19/2010 for the course ANTH 122 taught by Professor 323 during the Spring '10 term at Centennial College.
 Spring '10
 323

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