Bernoulli Differential Equation

Lecture slides covering Bernoulli differential equations — a first-order nonlinear ODE reducible to linear form.

Key Points

  • A Bernoulli DE has the form: $$ \frac{dy}{dx} + yP(x) = y^n Q(x) $$
  • Can be linearised by substituting $v = y^{1-n}$, reducing to a first-order linear DE solvable via integrating factor.

Examples Covered

  1. Example 1: $y(1 + xy^4),dx - dy = 0$ — find general solution.
  2. Example 2: $x,dy - (y + 5x^3 y^3),dx = 0$ — solve Bernoulli DE.
  3. Example 3: $y,dx + x(x^2 y - 1),dy = 0$ — show it is Bernoulli in $x$, find particular solution with $y(1) = 2$.

Links