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Solving ordinary differential equations
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With the introduction of differential operations to functions in analysis, equations representing the derivatives of unknown functions and the relationship between independent variables have entered the field of vision of mathematicians. This is a differential equation. The formation and development of differential equations are closely related to the development of science and technology such as mechanics, astronomy, and physics. Because in the real world, the movement of matter and its change laws are mathematically described by functional relationships, which means that the solution to the problem is to find a function that satisfies certain conditions, and such problems are converted into differential calculus Equation solving problems.
The basic idea of ??solving differential problems is similar to solving algebraic equations. It is necessary to find out the relationship between the known function and the unknown function in the problem, and then obtain one or several equations containing the unknown function, and then use Analytical methods are used to find expressions of unknown functions.
If the unknown function appearing in a differential equation contains only one independent variable, then this type of differential equation is an ordinary differential equation. The general solution of ordinary differential equations constitutes a family of functions, which mainly studies the classification and solution of equations or systems of equations, the existence and uniqueness of solutions, singular solutions, qualitative theory, etc.
Use ordinary differential equations to solve functionals and solve the fastest curve problem
Now, ordinary differential equations are used in automatic control, the design of various electronic devices, ballistic calculations, aircraft and missiles It has important applications in the study of flight stability and the study of chemical reaction process stability.