InterviewSolution
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InterviewSolution
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If `y=Acosn x+Bsinn x ,`show that `(d^2y)/(dx^2)+n^2 y=0`. |
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Answer» We have `y=A cos nx +B sin nx` `rArr (dy)/(dx)=(d)/(dx)(A cos nx)+(d)/(dx)(B sin nx)` `=-An sin nx+Bn cos nx` `=n(B cos nx-A sin nx)` `rArr (d^(2)y)/(dx^(2))=n.(d)/(dx)(B cos nx-A sin nx)` `=n.{B.(d)/(dx)(cosnx)-A.(d)/(dx)(sinnx)}` `=n.{-Bn sin nx-An cosnx}` `=-n^(2)(A cos nx+B sin nx)=-n^(2)y` `rArr(d^(2)y)/(dx^(2))+n^(2)y=0.` |
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