Balbharati Maharashtra State BoardStd 12 Commerce Statistics Part 1 Digest PdfChapter 8 Differential Equation and Applications Ex 8.4 Questions and Answers.
Maharashtra State Board 12th Commerce Maths Solutions Chapter 8 Differential Equation and Applications Ex 8.4
Solve the following differential equations:
Question 1
Maharashtra Board Solution
x dx + 2y dy = 0
Solution & Step-by-Step Answer:
x dx + 2y dy = 0 Integrating, we get ∫x dx + 2 ∫y dy = c1 ∴ ∴ x2 + 2y2 = c, where c = 2c1 This is the general solution.
Question 2
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 This is the general solution.
Question 3
Maharashtra Board Solution
x2y dx – (x3 + y3) dy = 0
Solution & Step-by-Step Answer:
x2y dx – (x3 + y3) dy = 0 ∴ (x3 + y3) dy = x2y dx ∴ ……(1) Put y = vx ∴ This is the general solution.
Question 4
Maharashtra Board Solution
Solution & Step-by-Step Answer:
This is the general solution.
Question 5
Maharashtra Board Solution
(x2 – y2) dx + 2xy dy = 0
Solution & Step-by-Step Answer:
(x2 – y2) dx + 2xy dy = 0 ∴ 2xy dy = -(x2 – y2) dx = (y2 – x2) dx ∴ ………(1)
Question 6
Maharashtra Board Solution
xy = x2 + 2y2
Solution & Step-by-Step Answer:
Question 7
Maharashtra Board Solution
x2 = x2 + xy – y2
Solution & Step-by-Step Answer:
