Exponential Growth and Decay 6.4. Separation of Variables When we have a first order differential equation which is implicitly defined, we can try to.

Slides:

Advertisements

Similar presentations

The Chain Rule Section 3.6c.

Advertisements

5 Copyright © Cengage Learning. All rights reserved. Logarithmic, Exponential, and Other Transcendental Functions.

Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.

Method Homogeneous Equations Reducible to separable.

Solving Systems Using Elimination. Elimination When neither equation is in the slope- intercept form (y =), you can solve the system using elimination.

Differential Equations There are many situations in science and business in which variables increase or decrease at a certain rate. A differential equation.

Solve the equation -3v = -21 Multiply or Divide? 1.

6.3 Separation of Variables and the Logistic Equation Ex. 1 Separation of Variables Find the general solution of First, separate the variables. y’s on.

BC Calculus – Quiz Review

Implicit Differentiation

Differential Equations. Definition A differential equation is an equation involving derivatives of an unknown function and possibly the function itself.

Reminder siny = e x + C This must be differentiated using implicit differentiation When differentiating y’s write dy When differentiating x’s write dx.

6.3 Separation of Variables and the Logistic Equation.

Solving a system of equations by adding or subtracting.

Warm-up It’s as easy as 1-2-3! 1)Start by separating variables. 2)Integrate both sides. 3) Solve for dy/dx. Solve = k(y – 80) This represents Newton’s.

First, a little review: Consider: then: or It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears.

Differential Equations and Slope Fields 6.1. Differential Equations  An equation involving a derivative is called a differential equation.  The order.

Differential Equations: Growth and Decay Calculus 5.6.

Differential Equations Sec 6.3: Separation of Variables.

Differential Equations

Separable Differential Equations

4.8 – Solving Equations with Fractions

7.3 Elimination Method Using Addition and Subtraction.

Two Step equations. Understand The Problem EX: Chris’s landscaping bill is 380$. The plants cost 212$,and the labor cost 48$ per hour. Total bill = plants.

One step equations Add Subtract Multiply Divide  When we solve an equation, our goal is to isolate our variable by using our inverse operations.  What.

Chapter 2 Solutions of 1 st Order Differential Equations.

Warm Up. Solving Differential Equations General and Particular solutions.

Differential equations and Slope Fields Greg Kelly, Hanford High School, Richland, Washington.

Ch. 7 – Differential Equations and Mathematical Modeling 7.4 Solving Differential Equations.

Solving First-Order Differential Equations A first-order Diff. Eq. In x and y is separable if it can be written so that all the y-terms are on one side.

Blue part is out of 50 Green part is out of 50  Total of 100 points possible.

Chapter 7.3.  Objective NCSCOS 4.03  Students will know how to solve a system of equations using addition.

Chapter 6 Integration Section 3 Differential Equations; Growth and Decay.

Do Now Solve using elimination: 3x + 2y = – 19 – 3x – 5y = 25.

Differential Equations 6 Copyright © Cengage Learning. All rights reserved.

Solving equations with variable on both sides Part 1.

* Collect the like terms 1. 2a = 2a x -2x + 9 = 6x z – – 5z = 2z - 6.

Solving 2 step equations. Two step equations have addition or subtraction and multiply or divide 3x + 1 = 10 3x + 1 = 10 4y + 2 = 10 4y + 2 = 10 2b +

Solving Equations with Variables on Both Sides. Review O Suppose you want to solve -4m m = -3 What would you do as your first step? Explain.

4-6 Solving Equations with Fractions What You’ll Learn ► To solve one – step equations ► To solve two – equations.

AP Calculus AB 6.3 Separation of Variables Objective: Recognize and solve differential equations by separation of variables. Use differential equations.

Section 9.4 – Solving Differential Equations Symbolically Separation of Variables.

Jeopardy Solving Equations

3. 3 Solving Equations Using Addition or Subtraction 3

Differential Equations

Specialist Mathematics

Section 3.3 Solving Equations with Variables on Both Sides

MTH1170 Differential Equations

Solving One Step Equations

Slope Fields & Differential Equations

Solving Systems Using Elimination

Part (a) Keep in mind that dy/dx is the SLOPE! We simply need to substitute x and y into the differential equation and represent each answer as a slope.

Differential Equations

Differential Equations Separation of Variables

6-3 Solving Systems Using Elimination

Do Now 1) t + 3 = – 2 2) 18 – 4v = 42.

Solving Two-Step Equations Lesson 2-2 Learning goal.

Exponential Functions: Differentiation and Integration

Objectives Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.

Solving Equations by Adding and Subtracting Solving Equations

Solving Multiplication Equations

Part (a) dy dx = 1+y x dy dx = m = 2

Math-7 NOTES What are Two-Step Equations??

Do Now Solve. 1. –8p – 8 = d – 5 = x + 24 = 60 4.

Section 6.3 Day 1 Separation of Variable

9.3 Separable Equations.

Slope Fields and Differential Equations

Presentation transcript:

Exponential Growth and Decay 6.4

Separation of Variables When we have a first order differential equation which is implicitly defined, we can try to use a method called separation of variables to solve the equation.

Separation of Variables Goal: get all y’s on one side (including dy) and all x’s on the other side (including dx). Once I have done this I integrate each side with respect to the appropriate variable and solve for y. Note: you MUST be multiplying each side by dy or dx. You cannot be adding, subtracting, or dividing.

Example Find the particular solution to the equation given that y=1 when x=1.

Example Given y(0) = 1, find the particular solution of.

Example Find the equation of the curve passing through (1, 3) that has a general slope of.

Example Find the general solution of.

Homework Pg 357 #1-10