Question:
Determine order and degree(if defined) of differential equation $\frac{d^{4} y}{d x^{4}}+\sin \left(y^{\prime \prime}\right)=0$
Solution:
$\frac{d^{4} y}{d x^{4}}+\sin \left(y^{\prime \prime \prime}\right)=0$
$\Rightarrow y^{\prime \prime \prime \prime}+\sin \left(y^{\prime \prime \prime}\right)=0$
The highest order derivative present in the differential equation is $y^{\prime \prime \prime}$. Therefore, its order is four.
The highest order derivative present in the differential equation is $y^{\prime \prime \prime}$. Therefore, its order is four.