Specialist Mathematics Solving differential equations DEs Solving differential

Solving differential equations › Verifying solutions. › First and second order when dy/dx is

General solution versus particular solution. Example: Find the general solution to general solution Particular

Classification of differential equations (DEs). THE ORDER OF EQUATION THE DEGREE OF EQUATION ›

Definitions and Terms A differential equation (diff. eq. , DE) is an equation that

Verifying solutions. https: //www. youtube. com/watch? v=p. AGFdf 2 t. Krc

Real life applications. • Population growth / decay, where rate of change of population

Ex 1. Verify that the given function is a solution to the given DE.

Ex 2. Verify that the given function is a solution to the given DE.

Ex 3. Find values for m that would make y = emx a solution

Practice Problem Verify that the DE is a solution to

Ex 9 A p 372 Questions 1 a, 2 c, d, e, g, 2

Slides: 13

Download presentation

Specialist Mathematics Solving differential equations (DEs).

Solving differential equations › Verifying solutions. › First and second order when dy/dx is the function of x. › First order when dy/dx is the function of y. › By separation of variables. › Using CAS. › Applications with DEs. Sketching slope fields and Euler’s method for numerical solutions of DEs.

General solution versus particular solution. Example: Find the general solution to general solution Particular solution requires boundary conditions. Example: Solve passes through (2, 0). given that the solution curve particular solution

Classification of differential equations (DEs). THE ORDER OF EQUATION THE DEGREE OF EQUATION › The highest derivative order that appears in a DE is called the order of the equation. › The highest power of a DE gives the degree. is a first order DE is a second order DE is a third order DE Linear and non-linear DEs.

Definitions and Terms A differential equation (diff. eq. , DE) is an equation that involves x, y, and some derivatives of y. These are called ordinary differential equations (ODEs) because y is a function of only x.

Verifying solutions. https: //www. youtube. com/watch? v=p. AGFdf 2 t. Krc

Real life applications. • Population growth / decay, where rate of change of population is proportional to the population at any time. • Newton’s Law of cooling – rate of change of temperature is proportional to the excess of the temperature above its surroundings. • Salt solutions type questions. • Rates in and rates out in a container. • DEs with related rates.

Ex 1. Verify that the given function is a solution to the given DE. DE Function Find dy/dx first Substitue back into the given DE Simpilfy LHS=RHS, verified. true so

Ex 2. Verify that the given function is a solution to the given DE. Notice that y = 0 is a solution to both DEs. This is called the trivial solution.

Ex 3. Find values for m that would make y = emx a solution of the DE 2 y + 7 y – 4 y = 0.

Practice Problem Verify that the DE is a solution to

Question 6 p 372

Ex 9 A p 372 Questions 1 a, 2 c, d, e, g, 2 c, g, 3, 4, 5, 7