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$\frac{x}{a}+\frac{y}{b}=1$

Differentiating both sides of the given equation with respect to x, we get:

$\frac{1}{a}+\frac{1}{b} \frac{d y}{d x}=0$

$\Rightarrow \frac{1}{a}+\frac{1}{b} y^{\prime}=0$

Again, differentiating both sides with respect to x, we get:

$0+\frac{1}{b} y^{\prime \prime}=0$

$\Rightarrow \frac{1}{b} y^{\prime \prime}=0$

$\Rightarrow y^{\prime \prime}=0$

Hence, the required differential equation of the given curve is $y^{\prime \prime}=0$.