Question

Find the order and the degree of the differential equation:

${[1+{\left(\frac{dy}{dx}\right)}^2]}^{\frac{3}{2}}=5\frac{d^{2}y}{d{x}^2}$.

Answer 1

Given the differential equation,

${[1+{\left(\frac{dy}{dx}\right)}^2]}^{\frac{3}{2}}=5\frac{d^{2}y}{d{x}^2}$

or, ${[1+{\left(\frac{dy}{dx}\right)}^2]}^3=25{\left(\frac{d^{2}y}{d{x}^2}\right)}^2$.

From the differential equation it is clear that the highest order term is the second order term on the right-hand side so the order of the differential equation is $2$ and the power of the highest order term is $2$ so degree of the differential equation is $2$.