Question

Write the order and the degree of the following differential equation :
$x^3{\left(\frac{d^{2}y}{d{x}^2}\right)}^2+x{\left(\frac{dy}{dx}\right)}^4=0$

Answer 1

Order of a differential equation is the order of the highest order derivative term present in the differential equation.
Degree of the differential equation is the power of that highest order derivative term.
Let us take the given differential equation
$x^3{\left(\frac{d^{2}y}{d{x}^2}\right)}^2+x{\left(\frac{dy}{dx}\right)}^4=0$
The highest order derivative term present is $\frac{d^{2}y}{d{x}^2}.$
Therefore, order is $2.$
The given differential equation is a polynomial equation in its derivative terms in which the highest order derivative term has power $2.$ Hence its degree is $2.$