Unformatted text preview: y 00 + 4 y = cos x, y (0) = 0 , y ( π ) = 0 . The general solution to the homogeneous equation y 00 + 4 y = 0 is C 1 cos 2 x + C 2 sin 2 x . We can use the method of undetermined coeﬃcients to ﬁnd the speciﬁc solution for this nonhomogeneous equation. Let Y ( x ) = A cos x + B sin x . Then Y 00 +4 Y = 3 A cos x +3 B sin x and hence A = 1 / 3 and B = 0. So our general solution here is C 1 cos 2 x + C 2 sin 2 x + 1 3 cos x . The ﬁrst boundary condition tells us that C 1 + 1 3 = 0, or C 1 =1 3 . The second tells us that C 11 3 = 0, or C 1 = 1 3 . It is not possible to satisfy both conditions at the same time, so there is no solution to the equation. 1...
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 Spring '07
 COSTIN
 Math, Differential Equations, Equations, Partial Differential Equations, Boundary value problem, c1 cos

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