# Bernoulli equation particular

• December 26th 2008, 08:38 AM
tenca
Bernoulli equation particular
Anyone can help me with this equation

dy/dx*(x^2*y^3+xy)=1

Thx

PS: I doubt that is a Bernoulli equation ?????
(Rofl)(Evilgrin)
• December 26th 2008, 09:51 AM
Jester
Quote:

Originally Posted by tenca
Anyone can help me with this equation

dy/dx*(x^2*y^3+xy)=1

Thx

PS: I doubt that is a Bernoulli equation ?????
(Rofl)(Evilgrin)

Actually it is! If we write the ODE as

$\frac{dy}{dx} = \frac{1}{x^2 y^3+xy}$

Then flip the equation

$\frac{dx}{dy} = x^2 y^3+xy$

and think of this as an equation for $x = x(y)$

make the substitution $x = \frac{1}{u}$ and it will become linear.