Bernoulli differential equation

[tracedinair]

Homework Statement

Solve the Bernoulli equation,

y'(x) - 4y(x) = 2e^(x) * sqrt(y(x))

Homework Equations

y' + P(x)y = Q(x)y^n - Bernoulli Eqn
e^(∫P(x) dx) - Integrating Factor

The Attempt at a Solution

y' - 4y = 2e^(x) * y^(1/2)

Divided both sides by y^(1/2)

y'/y^(1/2) - 4y/y^(1/2) = 2e^(x)

y'/y^(1/2) - 4y^(1/2) = 2e^(x)

My problem comes when changing variables. What am I supposed to choose for 'u' (the variable I'll be changing to)? Just y^(1/2)? My text and notes aren't very clear on this.

 

[rock.freak667]

Yes put u=y^1/2

In general, for:

$$\frac{dy}{dx}+P(x)y=Q(x)y^n$$

put $u=y^{1-n}$

 

[tracedinair]

Alright, thank you for your help.