Question

Arrange the following differential equations in increasing order on the basis of their order: 

Code	Differential Equation
A.	\(\dfrac{d^4y}{dx^4}+\sin\!\left(y'''\right)=0\)
B.	\(\left(\dfrac{d^5s}{dt^5}\right)^4+3s\dfrac{d^2s}{dt^2}=0\)
C.	\(y'''+2y''+y'=0\)
D.	\(y''+y=e^x\)

• A. D, B, A, C
• B. D,C,A,B
• C. B, D, C, A
• D. B, D, A, C

Hint:

Order of a differential equation is decided only by the highest order derivative present in it.

Answer 1

The Correct Option is B

Concept:
The order of a differential equation is the order of the highest derivative present in the equation.

Step 1: Find the order of A. \[ \frac{d^4y}{dx^4}+\sin(y''')=0 \] The highest derivative is: \[ \frac{d^4y}{dx^4} \] So, \[ \text{Order of A}=4 \]

Step 2: Find the order of B. \[ \left(\frac{d^5s}{dt^5}\right)^4+3s\frac{d^2s}{dt^2}=0 \] The highest derivative is: \[ \frac{d^5s}{dt^5} \] So, \[ \text{Order of B}=5 \]

Step 3: Find the order of C. \[ y'''+2y''+y'=0 \] The highest derivative is: \[ y''' \] So, \[ \text{Order of C}=3 \]

Step 4: Find the order of D. \[ y''+y=e^x \] The highest derivative is: \[ y'' \] So, \[ \text{Order of D}=2 \]

Step 5: Arrange in increasing order. \[ D=2,\quad C=3,\quad A=4,\quad B=5 \] Therefore, \[ D,C,A,B \] \[ \therefore \text{Correct order is } D,C,A,B \]