Question #fec67

1 Answer
Jan 26, 2018

This is Linear Differential Equation.
xy= ln(c/y)

Explanation:

Instead of dy/dx we form dx/dy because of linear x in Numerator.

y^2dx+(xy+1)dy=0

Dividing by dy

y^2dx/dy+(xy+1)=0

Dividing by y^2

dx/dy+(x/y+1/y^2)=0

dx/dy +x/y = -1/y^2

Comparing with:
dx/dy + P(y).x=Q(y)

P(y) = 1/y and Q(y) = -1/y^2

Integrating Factor:
e^(int 1/y dy)

e^lny

i.e y

Now,
x . IF = int IF . (-1/y^2) dy

x y = int y (-1/y^2) dy

x y = int -1/y dy

xy = -ln y + ln c

xy = ln(c/y)