Chapter 6 Differential Equations Ex 6.4

I. Solve the following differential equations:

Question 1.

Solution:

Question 2.

Question 3.

Solution:

Question 4.

Substituting these values in (1), we get

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.
x dy + 2y · dx = 0, when x = 2, y = 1
Solution:
∴ x dy + 2y · dx = 0
∴ x dy = -2y dx

Integrating, we get

This is the general solution.
When x = 2, y = 1, we get
4(1) = c
∴ c = 4

Question 13.

Question 14.

Question 15.

Solution: