Question

The order and degree of the differential equation $\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^{1/3}+x^{1/4}=0$ are respectively

• A. $2,3$
• B. $2,4$
• C. $3,3$
• D. $2,6$

Answer 1

Answer: (A)

$2,3$

the order and degree of the differential equation

$\frac{{\partial }_y}{\partial x^2}+{\left(\frac{\partial y}{\partial x}\right)}^{1/3+x^{1/4}=0}$ are respectively

$\frac{{\partial }^{2}y}{\partial x^2}+x^{1/4}=-{\left(\frac{\partial y}{\partial x}\right)}^{1/3}$

$\Rightarrow {\left(\frac{{\partial }^{2}y}{\partial x^2}\right)}^3+x^{3/4}+3{\left(\frac{{\partial }^{2}y}{\partial x^2}\right)}^2{x}^{1/4}+3\left(\frac{{\partial }^{2}y}{\partial x^2}\right)x^{2/4}=\frac{-\partial y}{\partial x}$

$\Rightarrow {\left(\frac{{\partial }^{2}y}{\partial x^2}\right)}^3+3{\left(\frac{{\partial }^{2}y}{\partial x^2}\right)}^2{x}^{1/4}+3\left(\frac{{\partial }^{2}y}{\partial x^2}\right)x^{2/4}+\frac{\partial y}{\partial x}+x^{3/4}=0$

Now since, the equation is in the normal form

we have order = 2

degree = 3.

Since, order = is the order of the highest order derivative

and degree = power of the highest order derivative