Bernoulli Differential Equation

[bioblade]

Homework Statement

Solve: 3dy/dx+y=(1-2x)y^4

Homework Equations

None, really.

The Attempt at a Solution

y'+y/3=((1-2x)/3)y^4

y'/y^4+1/3y^3=(1-2x)/3

w=1/y^3

w'=(-3/y^4)y'

w'/-3+w/3=(1-2x)/3

w'-w=2x-1

e^int(-dx)=e^-x

e^(-x)*w=-e^-x(2x-1)+c

w=1-2x+c*e^x

y^3=1/(1-2x+c*e^x)

wolfram alpha says it should be -1/(-c*e^x+2x+1) though. What did I do wrong?

 

[LCKurtz]

Homework Statement

Solve: 3dy/dx+y=(1-2x)y^4

Homework Equations

None, really.

The Attempt at a Solution

y'+y/3=((1-2x)/3)y^4

y'/y^4+1/3y^3=(1-2x)/3

w=1/y^3

w'=(-3/y^4)y'

w'/-3+w/3=(1-2x)/3

w'-w=2x-1

e^int(-dx)=e^-x

e^(-x)*w=-e^-x(2x-1)+c

Right there where you didn't show your work, you have a mistake in your integration.

w=1-2x+c*e^x

y^3=1/(1-2x+c*e^x)

wolfram alpha says it should be -1/(-c*e^x+2x+1) though. What did I do wrong?

 

[bioblade]

Ah, I got it now. Thanks!