Chapter Seven, Differential Equations

Knowledge logic structure diagram

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Postgraduate exam content

The basic concepts of ordinary differential equations, equations with separable variables, homogeneous differential equations, first-order linear differential equations, Bernoulli equations, total differential equations, some differential equations that can be solved by simple variable substitution, can be Lower-order higher-order differential equations, linear differential equations’ solution properties and solution structure theorems, second-order homogeneous linear differential equations with constant coefficients, some homogeneous linear differential equations with constant coefficients higher than the second-order, simple second-order constant Coefficient non-homogeneous linear differential equations, Euler equations, simple applications of differential equations.

Postgraduate exam requirements

1. Understand the concepts of differential equations and their orders, solutions, general solutions, initial value conditions and special solutions.
2. Master the equations of separable variables and the solution of first-order linear equations.
3. Be able to solve homogeneous equations, Bernoulli equations and total differential equations, and use simple variable substitution to solve some differential equations.
4. Will solve the following equations using the reduction method
5. Understand the nature of the solution of linear differential equations and the structural theorem of the solution.
6. Master the solution of second-order homogeneous linear differential equations with constant coefficients, and be able to solve some homogeneous linear differential equations with constant coefficients higher than the second order.
7. The free terms that can be solved are polynomials, exponential functions, sine functions, cosine functions, and their sum and product second-order non-homogeneous linear differential equations with constant coefficients.
8. Will solve Euler's equations.
9. Will use differential equations to solve some simple application problems.