InterviewSolution
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InterviewSolution
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Prove that `y=e^(x)+m` is a solution of the differential equation `(d^(2)y)/(dx^2)-(dy)/(dx)=0`, where `m` is a constant. |
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Answer» `y=e^(x)+m`……..`(1)` Differentiate with respect to `x` `(dy)/(dx)=e^(x)`……….`(2)` Again differentiate with respect to `x` `(d^(2)y)/(dx^(2))=e^(x)` `implies (d^(2)y)/(dx^(2))=(dy)/(dx)` [From eq. `(2)`] `implies (d^(2)y)/(dx^(2))-(dy)/(dx)=0` `:. y=e^(x)+m` is a solution of the given differential equation. |
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