Chapter 6 Differential Equations Ex 6.4

I. Solve the following differential equations:

Question 1.


Solution:

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Question 2.

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Question 3.

Solution:
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Question 4.
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Substituting these values in (1), we get
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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:

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Question 7.

Solution:

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Question 8.

Solution:

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Question 9.

Solution:

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Question 10.

Solution:

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

∴ x dy + 2y · dx = 0
∴ x dy = -2y dx
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Integrating, we get
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This is the general solution.
When x = 2, y = 1, we get
4(1) = c
∴ c = 4
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Question 13.
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Question 14.

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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