一阶微分方程解题方法指导（First order differential equations to guide the solution）.doc

一阶微分方程解题方法指导（First order differential equations to guide the solution） A first order differential equation is a guide Liu Bingjun In the high number of part ii, differential equation, the content of the chapter is independent and integral and series these contents have no contact, therefore, can be flexible teaching time, even before the speak multivariate function partial derivative teaching content of this chapter is also possible. A differential Equation is composed of unknown function and its derivative Equation. In the Equation containing the unknown function derivative of the highest order is called the differential equations of order. If the Equation solution containing arbitrary constant and the number is the same as the Equation of order number, said the solution for the general solution of differential equations. Satisfy certain initial conditions the solution of the solution for any constant. Its general solution to solve the differential Equation is or further special solution to meet certain conditions. This article focuses on a first order differential Equation of EMBED Equation. 3 to solve the problem. The equation of separable variables A first-order differential equation can be transformed into the following form: EMBED Equation. 3 (1) It is called an equation for separable variables. Assuming Equation (1), the EMBED Equation. 3 and EMBED Equation. 3 are continuous, then the solution of the Equation can be obtained on both sides of the Equation (1). The transformation of the equation into (1) is the key to solving the problem. (1) the general solution of the differential Equation, EMBED Equation. 3. Solution: the separation variable has to EMBED Equation. 3 Integrate both sides with the EMBED Equation. 3 The EMBED Equation. 3 EMBED Equation. 3 EMBED Equation. 3 2. The general solution of the differential Equation, EMBED Equation. 3. Solution: the separation variable has to EMBED Equation. 3 Integrate both sides with the EMBED Equation. 3 The EMBED E