Mathematics- Advanced Differential Equations-

Types Based on Order- First-Order Differential Equations, Second-Order Differential Equations, Higher-Order Differential Equations.

Types Based on Linearity- Linear Differential Equations, Non-linear Differential Equations.

Types Based on Functions- Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs).

Types Based on Special Techniques- Exact Differential Equations, Stochastic Differential Equations, Delay Differential Equations.

Types Based on Transform Methods- Differential Equations in the Laplace Domain, Differential Equations in the Fourier Domain.

Types Based on Applications- Mathematical Physics, Engineering and Control Theory, Biology and Medicine, Economics and Finance.

Advanced Topics- Nonlinear Systems of Differential Equations, Chaos Theory and Dynamical Systems, Variational Methods, Numerical Methods for Differential Equations.