# Bernoulli differential equation

1. Jan 22, 2009

### tracedinair

1. The problem statement, all variables and given/known data

Solve the Bernoulli equation,

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

2. Relevant equations

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

3. 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.

Last edited: Jan 22, 2009
2. Jan 22, 2009

### rock.freak667

Yes put u=y1/2

In general, for:

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

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

3. Jan 22, 2009

### tracedinair

Alright, thank you for your help.