Question

The order and degree of the differential equation

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

• A. $2,1$
• B. $1,2$
• C. $2,2$
• D. $1,1$

Answer 1

The correct option is A $2,1$

Given,

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

The above differential equation can be written as

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

It is clear that second order derivative terms are involved in the equation which is the highest order derivative term in the equation so order of the differential equation is $2$ and its power is $1$. So degree is $1$.