Chapter 8 Differential Equation and Applications Miscellaneous Exercise 8 Solutions

Balbharati Maharashtra State BoardStd 12 Commerce Statistics Part 1 Digest PdfChapter 8 Differential Equation and Applications Miscellaneous Exercise 8 Questions and Answers.

Maharashtra State Board 12th Commerce Maths Solutions Chapter 8 Differential Equation and Applications Miscellaneous Exercise 8

(I) Choose the correct option from the given alternatives:

(II) Fill in the blanks:

(III) State whether each of the following is True or False:

(IV) Solve the following:

(ii)
Solution:
The given differential equation is
This D.E. has highest order derivative with power 2.
∴ order = 1, degree = 2.

(ii)
Solution:

∴ from (1), the general solution is
y = x log x – x + c, i.e. y = x(log x – 1) + c.

(iii) dr = ar dθ – θ dr
Solution:
dr = ar dθ – θ dr
∴ dr + θ dr = ar dθ
∴ (1 + θ) dr = ar dθ
∴
On integrating, we get

∴ log |r| = a log |1 + θ| + c
This is the general solution.

(iv) Find the differential equation of the family of curves y = e^x(ax + bx²), where a and b are arbitrary constants.
Solution:
y = e^x(ax + bx²)
ax + bx²= ye^-x…….(1)
Differentiating (1) w.r.t. x twice and writing as y₁and as y₂, we get


This is the required differential equation.