Question

Consider the following statements
I. The order of the differential equation $\frac{dy}{dx}=e^X$ is $1$ .
II. The order of the differential equation $\frac{d^{2}y}{d{x}^2}+y=0$ is $2$ .
III. The order of the differential equation
$\left(\frac{d^{3}y}{d{x}^3}\right)+x^2{\left(\frac{d^{2}y}{d{x}^2}\right)}^3=0$ is $3$
Choose correct option.

• A. I and II are true
• B. II and III are true
• C. I and III are true
• D. All are true

Answer 1

Answer: (D)

I. The differential equation $\frac{dy}{dx}=e^x$
involves the highest derivative of first order.
$\therefore$ Its order is 1 .
II. The order of the differential equation
$\frac{d^{2}y}{d{x}^2}+y=0$
is 2 since it involves highest derivative of second order.
II. The differential equation
$\left(\frac{d^{3}y}{d{x}^3}\right)+x^2{\left(\frac{d^{2}y}{d{x}^2}\right)}^3=0$
involves highest derivative of third order
$\therefore$ Its order is 3 .