`y' + 3x^2y = x^2y^3` Solve the Bernoulli differential equation.

Expert Answers

An illustration of the letter 'A' in a speech bubbles


Multiply the above equation by `y^(-3)`



Taking the transformation  `v=y^(-2)`




Now the Bernoulli equation is transformed as ,



Now the above is a linear equation in the dependent variable v and independent variable y.

The integrating factor is n(x)=`e^(int(-6x^2dx))`










Let `t=x^3`





Substitute back `t=x^3`


Substitute back `v=y^(-2)`




 `y^2 = 1 / (1/3+Ce^(2x^3))`

`y = +-sqrt(3)/(Ce^(2x^3) + 1)`

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial