Chapter 6 Differential Equations Ex 6.4

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Chapter 6 Differential Equations Ex 6.4

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:

Maharashtra Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4 Q5
Maharashtra Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4 Q5.1
Maharashtra Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4 Q5.2

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:

Maharashtra Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4 Q15
Maharashtra Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4 Q15.1
Maharashtra Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4 Q15.2