Friday March 2 2018 MAT 146 Friday March

(A) What Does it Mean for Something to be a Solution to an Equation?

Differential Equation • A differential equation is an equation that contains one or more

Solution • A general solution to a differential equation is a family of functions

DE Questions y’ + 2 y = 2 ex Friday, March 2, 2018 MAT

DE Questions growing diminishing equilibrium values Friday, March 2, 2018 MAT 146

DE Questions Friday, March 2, 2018 MAT 146

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Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

(A) What Does it Mean for Something to be a Solution to an Equation? (i) Is x = − 1/5 a solution to the equation 4 x + 7 = 2 x – 3 ? (ii) State all solutions to the equation x 2 – x = 12. (iii) Is x = 4 a solution to the equation 3 ex = 12 ? (B) What Information About a Function is Revealed Through Its First Derivative? g’(x) = – 8 – 6 x 2. Gordon looked at the derivative of g(x) and shouted, “The function g is always decreasing!” How did he know? Friday, March 2, 2018 MAT 146

Differential Equation • A differential equation is an equation that contains one or more derivatives. • Here’s a differential equation you have already solved: y’ = 2 x What is the solution of this differential equation? Friday, March 2, 2018 MAT 146

Solution • A general solution to a differential equation is a family of functions that satisfies a given differential equation. • A particular solution to a differential equation (also called the solution to an initial-value problem) is a particular function that satisfies both a given differential equation and some specified ordered pair for the function. Friday, March 2, 2018 MAT 146

DE Questions y’ + 2 y = 2 ex Friday, March 2, 2018 MAT 146

DE Questions growing diminishing equilibrium values Friday, March 2, 2018 MAT 146

DE Questions Friday, March 2, 2018 MAT 146