For the following differential equation givne below indicate its order and degree (when defined)
$\frac{d^{4} y}{d x^{4}} - s i n \frac{d^{3} y}{d x^{3}} = 0$

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Solution

The given differential equations is
$\frac{d^{4} y}{d x^{4}} - s i n (\frac{d^{3} y}{d x^{3}}) = 0$
Since, the higest order derivative which occurs in the given differential equation is $\frac{d^{4} y}{d x^{4}}$ . Thus, order of the given equation is 4, as $s i n (\frac{d^{3} y}{d x^{3}})$ occurs in the equation is not a polynomial equation. Hence, degree is not defined.

Note:In any differential equation, if a derivative is not in a polynomial equation, then we can find the order but degree cannot be determined.

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Similar questions

For the following differential equation givne below indicate its order and degree (when defined)

$\frac{d^{2} y}{d x^{2}} + 5 x {(\frac{d y}{d x})}^{2} - 6 y = l o g x$

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$\frac{d^{4} y}{d x^{4}} - s i n \frac{d^{3} y}{d x^{3}} = 0$

\frac{d^{4} y}{d x^{4}} + s i n (\frac{d^{3} y}{d x^{3}}) = 0

For each of the differential equations given below, indicate its order and degree (if defined).

(i)

(ii)

(iii)

\frac{d^{4} y}{d x^{4}} + sin (\frac{d^{3} y}{d x^{3}}) = 0

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