Ordinary Differential Equations
Contents
--------------->>> First Order Differential Equation <<<---------------
Introduction
Separable form
Homogeneous form
Initial values
Exact form
Integration factor
Linear equation
Bernoulli equation
Riccati equation with variable coefficients
Exercise
--------------->>> Second Order Differential Equation <<<---------------
Reduction of order
Complementary function
Particular integral
Riccati equation with constant coefficients
Power series solution (Frobenius)
Exercise
--------------->>> High Order Differential Equation <<<---------------
General solution
Third order linear constant equation
Fourth order equation
Euler form
Exercise
--------------->>> System of first Order Differential Equation <<<---------------
Definition and types of forms
Autonomous system
Stability and classification of singular points
State space approach
Perturbation equation
Exercise
--------------->>> Laplace Transform <<<---------------
Properties and convolution theory
Differential and integro-differential equations
Laplace transform tablel
Exercise
--------------->>> Engineering Differential Equation <<<---------------
Mechanical vibrating system
Electrical system
Electromechanical system
Beams and bridges
Engineering systems
Exercise