InterviewSolution
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InterviewSolution
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यदि (If) `y=e^(x)(sinx+cosx)`, सिद्ध करें कि (prove that) `(d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0` |
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Answer» `y=e^(x)(sinx+cosx)` `rArr(dy)/(dx)=e^(x)*(sinx+cosx)+e^(x)(cosx-sinx)=2e^(x)cosx` `rArr(d^(2)y)/(dx^(2))=2[e^(x)cosx+e^(x)(-sinx)]` `=2e^(x)(cosx-sinx)` L.H.S. `=(d^(2)y)/(dx^(2))-2(dy)/(dx)+2y` `=2e^(x)(cosx-sinx)-2xx2e^(x)cosx+2e^(x)(sinx+cosx)` `=2e^(x)[cosx-sinx-2cosx+sinx+cosx]` `=2e^(x)xx0=0=` R.H.S. |
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