State the order and degree of the given differential equation, if the order is a and degree is b, find a+b?
$\frac{d^{2} y}{d x^{2}} = {[1 + {(\frac{d y}{d x})}^{2}]}^{3 / 2}$ .

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Solution

The correct option is A 4
Given differential equation is
$\frac{d^{2} y}{d x^{2}} = {[1 + {(\frac{d y}{d x})}^{2}]}^{3 / 2}$
Squaring both sides, we get
${(\frac{d^{2} y}{d x^{2}})}^{2} = {[1 + {(\frac{d y}{d x})}^{2}]}^{3}$
Here, the highest order derivative is of order 2 and its degree is 2.
So, the order of differential equation is 2 and the degree of a differential equation is 2.
$\Rightarrow a + b = 2 + 2 = 4$

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