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

Sum

Solve the following differential equation.

y dx + (x - y2 ) dy = 0

#### 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]

Concept: Differential Equations
Is there an error in this question or solution?

#### 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