(7) d'y dxª -2k² d²y dx² + ky=0 k is a non-zero constant. (This equation arises in bending of elastic plate problems) HINT: substitute y = Aerx to find roots of characteristic equations r₁= r2-k; and r3= r4=-k. Roots are repeated. ANSWER: y = Aekx+Bxekx+Ce-kx+Dxe-kx

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