Determine the order and degree of the following differential equation. State also whether it is linear or non-linear(Question 1-13)
Question 1.
Solution:
We have,
Order of function:
The Highest order of derivative of function is 3 i.e.,
So, the order of derivative is equal to 3.
Degree of function:
As the power of the highest order derivative of function is 1 (i.e., power of
is 1) So, degree of function is 1.
Linear or Non-linear:
The given equation is non-linear.
Question 2.
Solution:
We have,
Order of function:
As the highest order of derivative of function is 2.(i.e.,
) So, Order of the function is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 1(i.e., power of
is 1) So, Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is linear.
Question 3.
Solution:
We have,
Order of function:
As the highest order of derivative of function is 1 (i.e.,
) So, Order of the function is equal to 1.
Degree of function
As the power of the highest order derivative of the function is 3 (i.e., power of dy/dx is 3)
So, the degree of the function is equal to 3.
Linear or Non-linear:
The given equation is non-linear.
Question 4.
Solution:
We have,
On squaring both side, we get
On cubing both side, we get
Order of function:
As the highest order of derivative of function is 2 (i.e.,
So, Order of the function is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 2. (i.e., power of
is 2) So, the Degree of the function is equal to 2.
Linear or Non-linear:
The given equation is non-linear.
Question 5.
Solution:
We have,
Order of function:
As the highest order of derivative of function is 2
So, Order of the function is equal to 2.
Degree of function:
As the power of the highest order derivative of function is 1 (i.e., power of
is 1) So, the Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is non-linear.
Question 6.
Solution:
We have,
On cubing both side, we get
On squaring both side, we get
Order of function:
As the highest order of derivative of function is 2 (i.e.,
) So, the Order of the function is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 2(i.e., power of
is 2) So, the Degree of the function is equal to 2.
Linear or Non-linear:
The given equation is non-linear.
Question 7.
Solution:
We have,
On squaring both side, we get
Order of function:
The highest order of derivative of function is 4 (i.e.,
) So, the order of the derivative is equal to 4.
Degree of function:
As the power of the highest order derivative of the function is 2 (i.e., power of
is 2) So, the degree of function is 2.
Linear or Non-linear:
The given equation is non-linear.
Question 8:
Solution:
We have,
On squaring both side, we have
Order of function:
As the highest order of derivative of function is 1.
So, the Order of the function is equal to 1.
Degree of function:
As the power of the highest order derivative of the function is 1.
So, the degree of the function is equal to 1.
Linear or Non-linear:
The given equation is linear.
Question 9:
Solution:
We have,
Order of function:
As the highest order of derivative of function is 2 (i.e.,
) So, order of derivative is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 1 (i.e., power of
is 1) So, the Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is linear.
Question 10:
Solution:
We have,
Order of function:
As the highest order of derivative of the function is 2.
So, the Order of the function is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 1 (i.e., power of
is 1) So, the Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is non-linear.
Question 11:
Solution:
We have,
Order of function:
As the highest order of derivative of the function is 2
So, the Order of the function is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 3. (i.e., power of
is 3) So, the degree of the function is equal to 3.
Linear or Non-linear:
The given equation is non-linear.
Question 12:
Solution:
We have,
Order of function:
As the highest order of derivative of the function is 3
So, the Order of the function is equal to 3.
Degree of function:
As the power of the highest order derivative of the function is 1.(i.e., power of
is 1) So, the Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is non-linear.
Question 13:
Solution:
We have,
Order of function:
As the highest order of derivative of the function is 1
So, the Order of the function is equal to 1.
Degree of function:
As the power of the highest order derivative of the function is 1. (i.e., power of dy/dx is 1)
So, the Order of the function is equal to 1.
Linear or Non-linear:
The given equation is non-linear.