Suppose that the characteristic equation of the ODE L ( y ) = x 3 cos( x ) is gi

Question

Suppose that the characteristic equation of the ODE L(y) = x3 cos(x) is given by (r2 + 1)2 r3 = 0

We use the method of undermined coefficients to find a particular solution yp to the ODE. Select each correct statement below. Here p3 and q3 are 3rd order polynomials.

(1) The correct form of yp is x1[p3(x) sin(x) + q3(x) cos(x)]

(2) The correct form of yp is x2[p3(x) sin(x) + q3(x) cos(x)]

(3) The correct form of yp is x3[p3(x) sin(x) + q3(x) cos(x)]

(4) The correct form of yp is x2p3(x) sin(x)

(5) The correct form of yp is x2p3(x) cos(x)

Explanation / Answer

The correct form of yp is x2[p3(x) sin(x) + q3(x) cos(x)]

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