Bernoulli's Equation


Solve the following Bernoulli's differential equation or IVP.

  1.   \(y'+\dfrac{4}{x}\,y=x^3y^2, \: x > 0\)  solution

  2.   \( \displaystyle{x\frac{dy}{dx} + y = x^2y^2}\) solution

    3.  
  3. \( \displaystyle{\frac{dy}{dx} = y(xy^3-1)}\)    solution

  4.   \( \displaystyle{ x y' + y = \frac{1}{y^2}, \quad  y(1)=3}\)    solution