Question

The degree and order of the differential equation ${[1+2{\left(\frac{dy}{dx}\right)}^2]}^{3/2}=5\frac{d^{2}y}{d{x}^2}$ are

• A. $1,2$
• B. $2,2$
• C. $3,1$
• D. $4,3$

Answer 1

Answer: (B)

$2,2$

The order is the highest numbered derivative in the equation, While the degree is the highest power to which a derivatives is raised.
So, here we are given the equation as:
${[1+2{\left(\frac{dy}{dx}\right)}^2]}^{3/2}=5\frac{d^{2}y}{d{x}^2}$
${[1+2{\left(\frac{dy}{dx}\right)}^2]}^3={\left[5\frac{d^{2}y}{d{x}^2}\right]}^2$
Hence as we can see the order and degree for the above equation are 2, 2.