Write the sum of the order and degree of the following differential equation: $\frac{d}{d x} {{(\frac{d y}{d x})}^{3}} = 0$ .

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Solution

By using chain rule to evaluate the derivative on the left hand side, we get:
$\frac{d}{d x}$ { ${(\frac{d y}{d x})}^{3}$ } $= 0.$
$\Rightarrow 3 {(\frac{d y}{d x})}^{2} \frac{d^{2} y}{d x^{2}} = 0$

The order of this differential equation is $2$ because the highest order derivative appearing in the equation is second order.
The degree is the power of this highest order derivative. In this case degree is $1.$
So, the answer is $2 + 1 = 3.$

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