Question

Find order and degree (if defined) of the differential equation $\frac{d^{4}y}{d{x}^4}+sin\left(\frac{d^{3}y}{d{x}^3}\right)=0$.

Answer 1

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

Order of differential equation is the maximum times ${}^{\prime }{y}^{\prime }$ differentiated wrt $x$

$\frac{d^{4}y}{d{x}^4}$ ($4$ times $y$ differentiated wrt $x$)

$\Rightarrow$ order $=4$

$\Rightarrow$ degree $=$ power of highest order differential $=1\left(\frac{d^{4}y}{d{x}^4}\right)$