Question

The order and degree of the differential equation $y=x\frac{dy}{dx}+\sqrt{a^2{\left(\frac{dy}{dx}\right)}^2+b^2}$ is

• A. order $=1$, degree $=2$
• B. order $=2$, degree $=1$
• C. order $=2$, degree $=2$
• D. None of these

Answer 1

Answer: (A)

Given differential equation can be written as
$y^2+x^2{\left(\frac{dy}{dx}\right)}^2-2xy\frac{dy}{dx}$
$=a^2{\left(\frac{dy}{dx}\right)}^2+b^2$
Clearly, it is a 1st order and 2nd degree differential equation.