Question

Solve the differential equation: y dx + (x – y²)dy = 0

Answer 1

y dx + (x – y²)dy = 0

Reducing the given differential equation to the form `(dx)/(dy)` + Px = Q we get, `(dx)/(dy) + x/y` = y

I.F = `e^(intPdy)`

= `e^(int 1/y dy)`

= e^{log y}

= y

The general solution is given by 

x · IF = `int "Q" * "IF"  "dy"`

⇒ xy = `int "y"^2 "dy"`

⇒ xy = `"y"^3/3 + C`, which is the required general solution