1. This document discusses methods for solving first-order linear differential equations. It defines a first-order linear differential equation as one of the form y'+py=f(x).
2. It provides examples of solving homogeneous and non-homogeneous first-order linear differential equations. The general solutions are presented as y=Ce^-px + particular solutions.
3. Bernoulli differential equations of the form y'+py=f(x)y^n, n1 are introduced, which can be transformed into a first-order linear equation using a substitution. An example of solving a Bernoulli equation is shown.
This document discusses function derivatives and their calculation in several sections:
1. It defines the derivative of a function f(x) at a point x0 and provides formulas to calculate it.
2. It presents rules for finding derivatives of basic functions like polynomials, rational functions, and roots.
3. It introduces theorems for calculating derivatives of sums, products, and quotients of functions, as well as composite functions where one function is applied to another.
Examples are provided to demonstrate applying the rules and theorems to calculate derivatives.
1. This document discusses methods for solving first-order linear differential equations. It defines a first-order linear differential equation as one of the form y'+py=f(x).
2. It provides examples of solving homogeneous and non-homogeneous first-order linear differential equations. The general solutions are presented as y=Ce^-px + particular solutions.
3. Bernoulli differential equations of the form y'+py=f(x)y^n, n1 are introduced, which can be transformed into a first-order linear equation using a substitution. An example of solving a Bernoulli equation is shown.
This document discusses function derivatives and their calculation in several sections:
1. It defines the derivative of a function f(x) at a point x0 and provides formulas to calculate it.
2. It presents rules for finding derivatives of basic functions like polynomials, rational functions, and roots.
3. It introduces theorems for calculating derivatives of sums, products, and quotients of functions, as well as composite functions where one function is applied to another.
Examples are provided to demonstrate applying the rules and theorems to calculate derivatives.