Question

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

• 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

${[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^{3/4}=\frac{d^{2}y}{d{x}^2}$
$\Rightarrow {[1+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)]}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^4\cdots \left(1\right)$
The highest order derivative in the differential equation $\left(1\right)$ is $\frac{d^{2}y}{d{x}^2},$ so its order is $2.$

Equation $\left(1\right)$ is not a polynomial equation in $\frac{dy}{dx},$ so its degree is not defined.