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The P.I. of (D^2+1) y=cos〖3x 〗is * |
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Answer» The AUXILIARY equation is (m^2 +1)^2 = 0.The roots are +/- i , +/- i.The IMAGINARY roots are repeated.Hence the Complementary Function (CF) is (c1+c2 x)COS x + (c3+c4 x)sin x.The Particular Integral (PI) = [1/f(D)] cos 3X = [1/(D^2 +1)^2] cos 3xApplying the [1/f(D^2)] cos ax = [1/f(-a^2)]cos axwe get [1/64] cos 3xHence the complete solution is = CF +PI= (c1+c2 x)cos x + (c3+c4 x)sin x + [1/64] cos 3x |
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