Balbharti12th Maharashtra State Board Maths Solutions BookPdf Chapter 6 Differential Equations Ex 6.4 Questions and Answers.
Maharashtra State Board 12th Maths Solutions Chapter 6 Differential Equations Ex 6.4
I. Solve the following differential equations:
Question 1
Maharashtra Board Solution
Solution & Step-by-Step Answer:
Question 2
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(x2 + y2) dx – 2xy. dy = 0
Solution & Step-by-Step Answer:
(x2 + y2) dx – 2xy dy = 0 ∴ 2xy dy = (x2 + y2) dx ∴ ………(1)
Question 3
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Solution & Step-by-Step Answer:
Question 4
Maharashtra Board Solution
y2 dx + (xy + x2) dy = 0
Solution & Step-by-Step Answer:
y2 dx + (xy + x2) dy = 0 ∴ (xy + x2) dy = -y2 dx ∴ ……..(1) Put y = vx ∴ Substituting these values in (1), we get
Question 5
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(x2 – y2) dx + 2xy dy = 0
Solution & Step-by-Step Answer:
Question 6
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Solution & Step-by-Step Answer:
Question 7
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Solution & Step-by-Step Answer:
Question 8
Maharashtra Board Solution
Solution & Step-by-Step Answer:
Question 9
Maharashtra Board Solution
Solution & Step-by-Step Answer:
Question 10
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xy = x2 + 2y2, y(1) = 0
Solution & Step-by-Step Answer:
Question 11
Maharashtra Board Solution
x dy + 2y · dx = 0, when x = 2, y = 1
Solution & Step-by-Step Answer:
∴ 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 ∴ the particular solution is x2y = 4.
Question 12
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x2 = x2 + xy + y2
Solution & Step-by-Step Answer:
x2 = x2 + xy + y2 ∴ ………(1) Put y = vx ∴
Question 13
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(9x + 5y) dy + (15x + 11y) dx = 0
Solution & Step-by-Step Answer:
(9x + 5y) dy + (15x + 11y) dx = 0 ∴ (9x + 5y) dy = -(15x + 11y) dx ∴ ………(1) Put y = vx ∴
Question 14
Maharashtra Board Solution
(x2 + 3xy + y2) dx – x2 dy = 0
Solution & Step-by-Step Answer:
(x2 + 3xy + y2) dx – x2 dy = 0 ∴ x2 dy = (x2 + 3xy + y2) dx ∴ ………(1)
Question 15
Maharashtra Board Solution
(x2 + y2) dx – 2xy dy = 0.
Solution & Step-by-Step Answer:
