Question

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

• A. 1, 1
• B. 1, 2
• C. 1, 3
• D. 2, 1
• E. 2, 2

Answer 1

Answer: (E)

Given differential equation is
$\frac{d^{2}Y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^{3/2}=Y$
or${\left(\frac{dy}{dx}\right)}^{3/2}=\left(y-\frac{d^{2}y}{d{x}^2}\right)$
On squaring both sides, we get
${\left(\frac{dy}{dx}\right)}^3={\left(y-\frac{d^{2}y}{d{x}^2}\right)}^2$
$\Rightarrow {\left(\frac{dy}{dx}\right)}^3=y^2+{\left(\frac{d^{2}y}{d{x}^2}\right)}^2-2y\frac{d^{2}y}{d{x}^2}$
Here, the highest order derivative is $2$, whose degree is $2$ .