Question

The order and degree of the differential equation $\frac{d^{3}y}{d{x}^3}-3\frac{d^{2}y}{d{x}^2}+2{\left(\frac{dy}{dx}\right)}^4=y^4$ ____________ and ___________ respectively.

Answer 1

Given: $\frac{d^{3}y}{d{x}^3}-3\frac{d^{2}y}{d{x}^2}+2{\left(\frac{dy}{dx}\right)}^4=y^4$

Here, the order of the differential equation is 3.

And the power of the highest order derivative is 1.

Hence, the order and degree of the differential equation $\frac{d^{3}y}{d{x}^3}-3\frac{d^{2}y}{d{x}^2}+2{\left(\frac{dy}{dx}\right)}^4=y^4$ is 3 and 1 respectively.