Question
For each of the differential equations given below, indicate its order and degree (if defined).
$​​\frac{\text{d}^4\text{y}}{\text{dx}^4}-\sin\Big(\frac{\text{d}^3\text{y}}{\text{dx}^3}\Big)=0$

Answer

Given: Differential equation $​​\frac{\text{d}^4\text{y}}{\text{dx}^4}-\sin\Big(\frac{\text{d}^3\text{y}}{\text{dx}^3}\Big)=0$
The highest order derivative present in this differential equation is $\frac{\text{d}^4\text{y}}{\text{dx}^4}$ and hence order of this differential equation if 4.
The given differential equation is a polynomial equation in derivatives therefore, degree of this differential equation is not defined.
Therefore, order = 4, Degree not defined

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