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# Determine order and degree(if defined) of differential equation

Question:

Determine order and degree(if defined) of differential equation $y^{\prime \prime}+2 y^{\prime}+\sin y=0$

Solution:

$y^{\prime \prime}+2 y^{\prime}+\sin y=0$

The highest order derivative present in the differential equation is $y^{\prime \prime}$. Therefore, its order is two.

This is a polynomial equation in $y^{\prime \prime}$ and $y^{\prime}$ and the highest power raised to $y^{\prime \prime}$ is one. Hence, its degree is one.