Question

The differential equation $1+\frac{dy}{dx}-{\left(\frac{d^{2}y}{d{x}^2}\right)}^{3/2}=0$ is of

• A. Order $1$ & degree $2$
• B. Order $2$ & degree $3$
• C. Order $3$ & degree $6$
• D. Order $3$ & degree $3$

Answer 1

The correct option is B Order $2$ & degree $3$

Given the differential equation differential equation $1+\frac{dy}{dx}-{\left(\frac{d^{2}y}{d{x}^2}\right)}^{3/2}=0$ can be written as,

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

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

From this equation it is clear that the highest ordered term present in the equation is a second ordered term so the order of the differential equation is $2$ and the degree of the highest order term is $3$ so degree of the differential equation is $3$.