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Question

For the question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

y=ex+1 and y''-y'=0.

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Solution

Given, y=ex+1
On differentiating both sides of this equation w.r.t. x, we get
y=ddx(ex+1)=ex ....(i)
Again differentiating both sides w.r.t. x, we get
y′′=ddx(ex)=exy′′=ex
On substituting the values of y' and y'' in the given differential equation,
LHS=y′′y=exex=0=RHS
Hence, y=ex+1 is a solution of the given differential equation.


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