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Verify that the given functions (explic...

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:`y=e^x+1:yprimeprime-yprime=0`

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Given, : `y=e^(x)+1`…….`(1)`
differentiate w.r.t.x,
`(dy)/(dx)=e^(x)`………`(2)`
Again, differentiate w.r.t.x,
`(d^(2)y)/(dx^(2))=e^(x)`
`implies (d^(2)y)/(dx^(2))=(dy)/(dx)` [from equation `(2)`]
`implies (d^(2)y)/(dx^(2))-(dy)/(dx)=0`
Therefore, `y=e^(x)+1` is the solution of given differential equation.
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