Question

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

• 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

The correct option is D order$=2$; degree $=$ not defined

We have, ${[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^{3/4}=\frac{d^{2}y}{d{x}^2}$

Take forth power both sides,

${[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^4$

Clearly above differential equation is not a polynomial equation in differential coefficient

Hence degree is not defined

But the order is the highest order of differential term which is $2$ here.