Класс 12 Решения RD Sharma – Глава 22 Дифференциальные уравнения – Упражнение 22.1 | Набор 2
Определите порядок и степень следующего дифференциального уравнения. Укажите также, является ли оно линейным или нелинейным (вопрос 14-26).
Вопрос 14. 
Решение :
We have,
Oder of function:
As the highest order of derivative of function is 1 (i.e., dy/dx)
So, the order of the derivative 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 degree of function is 1.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 15. 
Решение:
We have,
On cubing both side, we have
Order of function:
The Highest order of derivative of function is 2. (i.e.,
)
So, the order of the derivative is equal to 2.
Degree of function:
As the power of the highest order derivative of the function is 3 (i.e., power of
So, the degree of function is 3.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 16. 
Решение:
We have,
Squaring both sides, we have
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
So, the Degree of the function is equal to 2.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 17. 
Решение:
We have,
One squaring both side, we have
Order of function:
As the highest order of derivative of the 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
So, the Degree of the function is equal to 2.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 18. 
Решение:
We have,
On squaring both sides, we get
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 2.(i.e., power of dy/dx is 2)
So, the Degree of the function is equal to 2.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 19. 
, где p = dy/dx
Решение:
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 2 (i.e., power of dy/dx is 2)
So, the Degree of the function is equal to 2.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 20: dy/dx + e y = 0
Решение :
We have,
dy/dx + ey = 0
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 Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 21. 
Решение :
We have,
Order of function:
As the highest order of derivative of the function is 2
So, the order of the derivative is equal to 2.
Degree of function:
is not a polynomial function. So degree can not be defined.
So, the degree of function is not defined.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 22. (у") 2 + (у') 3 + siny = 0
Решение:
We have,
(y”)2 + (y’)3 + siny = 0
Where
Order of function:
The highest order of derivative of the function is 2. (i.e., y”)
So, the order of the derivative is equal to 2.
Degree of function
As the power of the highest order derivative of the function is 2 (i.e., power of y” is 2)
So, the degree of function is 2.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 23. 
Решение:
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
So, the Degree of the function is equal to 1.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 24. 
Решение:
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 linear.
Вопрос 25. 
Решение:
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.
The degree of function:
is not a polynomial function. So degree can not be defined.
So, the degree of function is not defined.
Linear or Non-linear:
The given equation is non-linear.
Вопрос 26. 
Решение:
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 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.