Question

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