Solve the following differential equation. y dx + (x - y 2 ) dy = 0 - Mathematics and Statistics

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Sum

Solve the following differential equation.

y dx + (x - y2 ) dy = 0

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Solution

y dx + (x - y2 ) dy = 0

∴ y dx = (y2 - x) dy

∴ `dx/dy = (y^2 - x) /y=  y - x/y `

∴ `dx/dy + x/y = y`

The given equation is of the form

`dx/dy + Px = Q`

where, P = `1/y` and Q = y

∴ I.F. = `e int^ (pdy) = e int ^(1/ydy) = e ^(log |y|)= y`

∴ Solution of the given equation is

`x (I.F.) =int Q (I.F.) dy + c_1`

∴  `xy = int y(y) dy = y^3/3 + c_1`

∴  3xy = y3 + c   …[3c1 = c]

  Is there an error in this question or solution?
Chapter 8: Differential Equation and Applications - Exercise 8.5 [Page 168]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.5 | Q 1.5 | Page 168

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