we have,$y=e^x...(1)$
Differentiating both sides of $(1)$
with respect to $x,$ we get
$=\frac{\text{dy}}{\text{dx}}=\text{e}^{\text{x}}$
$=\frac{\text{dy}}{\text{dx}}=\text{y} [$Using $(1)]$
It is the given differential equation.
Here, $y = ex$ satisfies the given differential equation;
hence, it is a solution.
Also, when $x = 0, y = e^{0}= 1,$ i.e. $y\ (0) = 1$
Hence, $y = e^x$ is the solution to the given initial value problem.
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