Bernoulli's Differential Equations — Study Resources & PYQs

Solution of Bernoulli-type first-order differential equations.

Study resources

Paul's Online Math Notes - Bernoulli Differential Equations (Article) — Complete derivation of the substitution v = y^(1-n) that reduces a Bernoulli equation to a linear one, followed by fully worked examples.
Ordinary Differential Equation - GP Sir (Video) — The original ODE playlist with a very large number of solved Bernoulli-equation problems. Use it for extra practice after the 2.0 playlist.
Wikipedia - Bernoulli differential equation (Article) — Defines Bernoulli's equation dy/dx + Py = Qy^n and shows the substitution z = y^(1-n) that reduces it to a linear equation.
Linear Differential Equations - Unacademy course (Divyasha Sinha) (Video) — A 21-lesson IIT-JAM course working through homogeneous/exact/linear/Bernoulli first-order equations, integrating factors, higher-order linear equations with constant coefficients, complementary funct…
Paul's Online Math Notes - Exact Equations (Article) — Gives the exactness test (dM/dy = dN/dx) and the full solution procedure with detailed examples. Read this along with the integrating factor rules from your textbook for the non-exact case.
MIT OpenCourseWare — Fourier Series and Partial Differential Equations (Article) — MIT course materials covering Fourier series and partial differential equations.

ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
ENGINEERING MATHEMATICS-II — BMAT21 · Government College of Engineering and Technology, Jammu
Engineering Mathematics-II — BMAT21 · Government College of Engineering and Technology, Jammu
Engineering Mathematics-II — BST1201 · Government College of Engineering and Technology, Jammu
Engineering Mathematics-II — BST1201 · Government College of Engineering and Technology, Jammu