Question

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

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

Answer 1

The correct option is E $2,2$

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

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

Squaring both sides, we get

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

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

Power of highest derivative is 2.

Order$=2$ and degree$=2$