Bernoulli equations

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Intros
Lessons
  1. What are Bernoulli Equations and how are they solved?
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Examples
Lessons
  1. Solving Bernoulli Equations
    Rewrite the following Bernoulli equations so that they are solvable via the integrating factor technique:
    1. dydx+(x2+1)y=3y2 \frac{dy}{dx}+(x^2+1)y=3y^2
    2. dydx+y(2e2x+x)=cos(x)y5\frac{dy}{dx}+ y(2e^{2x}+ \sqrt{x})= \cos (x)y^5
  2. Explicitly solve the following Differential Equation:

    dydx+1xy=y3\frac{dy}{dx}+\frac{1}{x} y=y^3

    With initial conditions y(12=1)y(\frac{1}{2}=1)