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