Balbharti12th Maharashtra State Board Maths Solutions BookPdf Chapter 6 Differential Equations Ex 6.1 Questions and Answers.
Maharashtra State Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.1
1. Determine the order and degree of each of the following differential equations:
Question (i).
Solution:
The given D.E. is
This D.E. has highest order derivative with power 1.
∴ the given D.E. is of order 2 and degree 1.
Question (ii).
Solution:
The given D.E. is
On cubing both sides, we get
This D.E. has highest order derivative with power 3.
∴ the given D.E. is of order 2 and degree 3.
Question (iii).
Solution:
The given D.E. is
∴ = 2 sin x + 3
This D.E. has highest order derivative with power 2.
∴ the given D.E. is of order 1 and degree 2.
Question (iv).
Solution:
The given D.E. is
On squaring both sides, we get
This D.E. has highest order derivative with power 1.
∴ the given D.E. has order 3 and degree 1.
Question (v).
Solution:
The given D.E. is
This D.E. has highest order derivative with power 1.
∴ the given D.E. has order 2 and degree 1.
Question (vi).
(y”‘)2 + 3y” + 3xy’ + 5y = 0
Solution:
The given D.E. is (y”‘)2 + 3y” + 3xy’ + 5y = 0
This can be written as:
This D.E. has highest order derivative with power 2.
∴ The given D.E. has order 3 and degree 2.
Question (vii).
Solution:
The given D.E. is
This D.E. has highest order derivative
∴ order = 2
Since this D.E. cannot be expressed as a polynomial in differential coefficients, the degree is not defined.
Question (viii).
Solution:
The given D.E. is
On squaring both sides, we get
This D.E. has highest order derivative with power 2.
∴ the given D.E. has order 2 and degree 2.
Question (ix).
Solution:
The given D.E. is
∴
This D.E. has highest order derivative with power 3.
∴ the given D.E. has order 3 and degree 3.
Question (x).
Solution:
The given D.E. is
On squaring both sides, we get
This D.E. has highest order derivative with power 1.
∴ the given D.E. has order 2 and degree 1.
