Question

Find the order and degree of the differential equation $\left[1+ \left(\frac{dy}{dx}\right)^{2 } +\sin \left(\frac{dy}{dx}\right)\right]^{\frac{3}{4}} = \frac{d^{2}y}{dx^{2}}$

• A. order=2
  degree=3
• B. order=2
  degree=4
• C. order=2
  degree=$\frac{3}{4}$
• D. order=2
  degree= not defined

Answer 1

Answer: (D)

We have, $\left[1+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)\right]^{3 / 4}=\frac{d^{2} y}{d x^{2}}$
$\Rightarrow \left(\frac{d^{2} y}{d x^{2}}\right)^{4}=\left[1+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)\right]^{8}$
Clearly, order $=2$ and degree $=$ not defined