For the following differential equation givne below indicate its order and degree (when defined)
${(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y = s i n x$

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Solution

The given differential equations is
${(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y = s i n x \Rightarrow {(\frac{d y}{d x})}^{3} - 4 {(\frac{d y}{d x})}^{2} + 7 y - s i n x = 0$
As the highest order derivative that occurs in the given differential equation is $\frac{d y}{d x},$ thus order of the equations is 1 and its degree is 3.
$(∵ T h e h i g h e s t p o w e r o f \frac{d y}{d x}, w h i c h o c c u r s (\frac{d y}{d x}))$

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

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(ii)

(iii)

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