Separable ODEs

Basic concepts of differential equations: Definition of differential equation, order of differential equation, degree of differential equation, general solution and particular solution.

Separable differential equations: Definition of separable differential equations, solving separable differential equations, and example problems.

Homogeneous differential equations: Definition of homogeneous differential equations, solving homogeneous differential equations, and example problems.

Non-homogeneous differential equations: Definition of non-homogeneous differential equations, solving non-homogeneous differential equations, and example problems.

First-order linear differential equations: Definition of first-order linear differential equations, solution of first-order linear differential equations, and example problems.

Second-order linear differential equations: Definition of second-order linear differential equations, solution of second-order linear differential equations, and example problems.

Applications of separable differential equations: Problems related to population growth, decay, and radioactive decay along with the concept of logistic growth.

Laplace Transform: Definition of Laplace transform, solving differential equations using Laplace transform, and example problems.

Power series solution of differential equations: Definition of power series solution of differential equations, solving differential equations using power series, and example problems.

Numerical methods for differential equations: Euler's method, Runge-Kutta method, and example problems.

Homogeneous Separable ODE: An ODE of the form f(y)dy=g(x)dx where f and g are continuous functions.

Inhomogeneous Separable ODE: An ODE of the form y’=f(x)g(y)+h(x).

Linear Separable ODE: A first order linear ODE that can be written in the form y′+p(x)y=q(x), where p(x) and q(x) are continuous functions.

Exact ODE: A first order ODE that can be written in the form M(x,y)dx+N(x,y)dy=0, where M and N are continuous functions and M_y=N_x.

Bernoulli's Separable ODE: A first order ODE of the form y′+p(x)y=q(x)y^n with n≠0,1.

Riccati's Separable ODE: A first order ODE of the form y′=a(x)y^2+b(x)y+c(x), where a, b, and c are continuous functions.

Nonlinear Separable ODE: A first order ODE of the form y′=f(x)g(y).

Lagrange's Linear ODE: A second order ODE of the form y′′+λ(x)y=0, where λ(x) is a continuous function.

Euler's Homogeneous ODE: A second order ODE of the form x^2 y''+ axy'+ by=0, where a and b are constants.

Airy's ODE: A second order ODE of the form y′′- xy=0.

Bessel's ODE: A second order ODE of the form x^2 y''+ xy'+ (x^2-n^2)y=0.

Legendre's ODE: A second order ODE of the form (1- x^2)y′′- 2xy′+ n(n+1)y=0.

Hypergeometric's ODE: a second order ODE of the form x(1-x)y''+[(c-a-b)x: C]y'+ aby=0, where a, b, and c are constants.